Dissertations / Theses on the topic 'Abelian surfaces'

In this thesis we produce a generating function for the number of hyperelliptic curves (up to translation) on a polarized Abelian surface using the crepant resolution conjecture and the Yau-Zaslow formula. We present a formula to compute these in terms of P. A. MacMahon's generalized sum-of-divisors functions, and prove that they are quasi-modular forms.

A key property of projective varieties is the very ampleness of line bundles as this provides embeddings into projective space and allows us to express the variety in equational terms. In this thesis we study the general version of this property which is k- very ampleness of line bundles. We introduce the notation of critical k-very ampleness and compute it for abelian surfaces. The property of k-very ampleness is usually discussed using tools from divisor theory but we take a different approach and use methods from derived algebraic geometry as part of program to use properties of the derived category of a variety to access the geometry of the variety. In particular, we use the Fourier-Mukai transform, moduli spaces of sheaves and properties of Bridgeland stability. We compute walls for certain Bridgeland stable spaces and certain Chern characters and to complete the picture we study the moduli spaces of torsion sheaves with minimal first Chern class and we go on to compute the walls for these as well building on tools developed earlier in the thesis.

Dans cette thèse nous étudions deux problèmes. Le premier est la non-existence de pointsrationnels non spéciaux sur des quotients d’Atkin-Lehner de courbes de Shimura. Le se-cond est l’absence de surfaces abéliennes rationnelles à multiplication potentiellementquaternioniques munies d’une structure de niveau. Ces deux problèmes sont liés car unesurface abélienne rationnelle simple à multiplication potentiellement quaternionique cor-respond à un point rationnel non spécial sur un certain quotient d’Atkin-Lehner de courbede Shimura.Dans une première partie nous expliquons comment vérifier un critère de Parent etYafaev en grande généralité pour prouver que dans les conditions du cas non ramifié deOgg, et si p est assez grand par rapport à q, alors le quotient X^pq/w_q n’a pas de pointrationnel non spécial.Dans une seconde partie nous déterminons une borne effective pour les structures deniveaux possibles pour une surface abélienne rationnelle acquérant sur un corps quadra-tique imaginaire fixé multiplication par un ordre fixé dans une algèbre de quaternions
In this thesis we study two problems. The first one is the non-existence of rational non-special points on Atkin-Lehner quotients of Shimura curves. The second one is the absence of rational abelian surfaces with potential quaternionique multiplication endowed with a level structure. These two problems are linked because a simple rational abelian surface with potential quaternionique multiplication is associated to a rational non-special point on an Atkin-Lehner quotients of Shimura curve. In a first part of our work we explain how to verify in wide generality a criterium of Parent and Yafaev in order to prove that in the conditions of Ogg's non ramified case, and if $p$ is big enough compared two $q$, then the quotient $X^{pq}/w_q$ has no non-special rational point. In a second part we determine an effective born for possible level structures on rational abelian surfaces having, over a fixed quadratic field, multiplication by a fixed order in a quaternion algebra

Bei elliptischen Kurven E/K über einem Zahlkörper K zwingt die Cassels-Tate Paarung die Ordnung der Tate-Shafarevich Gruppe Sha(E/K) zu einem Quadrat. Ist A/K eine prinzipal polarisierte abelschen Varietät, so ist bewiesen, daß die Ordnung von Sha(A/K) ein Quadrat oder zweimal ein Quadrat ist. William Stein vermutet, daß es für jede quadratfreie positive ganze Zahl k eine abelsche Varietät A/Q gibt, mit #Sha(A/Q)=kn². Jedoch ist es ein offenes Problem was zu erwarten ist, wenn die Dimension von A/Q beschränkt wird. Betrachtet man ausschließlich abelsche Flächen B/Q, so liefern Resultate von Poonen, Stoll und Stein Beispiele mit #Sha(B/Q)=kn², für k aus {1,2,3}. Diese Arbeit studiert tiefgehend nicht-einfache abelsche Flächen B/Q, d.h. es gibt elliptische Kurven E_1/Q und E_2/Q und eine Isogenie phi: E_1 x E_2 -> B. Relativ zur quadratischen Ordnung der Tate-Shafarevich Gruppe von E_1 x E_2 soll die Ordnung von Sha(B/Q) bestimmt werden. Um dieses Ziel zu erreichen wird die Isogenie-Invarianz der Vermutung von Birch und Swinnerton-Dyer ausgenutzt. Für jedes k aus {1,2,3,5,6,7,10,13,14} wird eine nicht-einfache, nicht-prinzipal polarisierte abelsche Fläche B/Q konstruiert, mit #Sha(B/Q)=kn². Desweiteren wird computergestützt berechnet wie oft #Sha(B/Q)=5n², sofern die Isogenie phi: E_1 x E_2 -> B zyklisch vom Grad 5 ist. Es stellt sich heraus, daß dies bei circa 50% der ersten 20 Millionen Beispielen der Fall ist. Abschließend wird gezeigt, daß wenn phi: E_1 x E_2 -> B zyklisch ist und #Sha(B/Q)=kn², so liegt k in {1,2,3,5,6,7,10,13}. Bei allgemeinen Isogenien phi: E_1 x E_2 -> B bleibt es unklar, ob k nur endlich viele verschiedene Werte annehmen kann. Im Anhang wird auf abelsche Flächen eingegangen, welche isogen zu der Jacobischen J einer hyperelliptischen Kurve über Q sind. Mit den in dieser Arbeit entwickelten Techniken können, anhand gewisser zyklischer Isogenien phi: J -> B, für jedes k in {11,17,23,29} Beispiele mit #Sha(B/Q)=kn² gegeben werden.
For elliptic curves E/K over a number field K the Cassels-Tate pairing forces the order of the Tate-Shafarevich group Sha(E/K) to be a perfect square. It is known, that if A/K is a principally polarised abelian variety, then the order of Sha(A/K) is a square or twice a square. William Stein conjectures that for any given square-free positive integer k there is an abelian variety A/Q, such that #Sha(A/Q)=kn². However, it is an open question what to expect if the dimension of A/Q is bounded. Restricting to abelian surfaces B/Q, then results of Poonen, Stoll and Stein imply that there are examples such that #Sha(B/Q)=kn², for k in {1,2,3}. In this thesis we focus in depth on non-simple abelian surfaces B/Q, i.e. there are elliptic curves E_1/Q and E_2/Q and an isogeny phi: E_1 x E_2 -> B. We want to compute the order of Sha(B/Q) with respect to the order of the Tate-Shafarevich group of E_1 x E_2, which has square order. To achieve this goal, we explore the invariance under isogeny of the Birch and Swinnerton-Dyer conjecture. For each k in {1,2,3,5,6,7,10,13,14} we construct a non-simple non-principally polarised abelian surface B/Q, such that #Sha(B/Q)=kn². Furthermore, we compute numerically how often the order of Sha(B/Q) equals five times a square, for cyclic isogenies phi: E_1 x E_2 -> B of degree 5. It turns out that this happens to be the case in approx. 50% of the first 20 million examples we have checked. Finally, we prove that if there is a cyclic isogeny phi: E_1 x E_2 -> B and #Sha(B/Q)=kn², then k is in {1,2,3,5,6,7,10,13}. For general isogenies phi: E_1 x E_2 -> B it remains unclear, whether there are only finitely many possibilities for k. In the appendix, we briefly consider abelian surfaces B/Q being isogenous to Jacobians J of hyperelliptic curves over Q. The techniques developed in this thesis allow to understand certain cyclic isogenies phi: J -> B. For each k in {11,17,23,29}, we provide an example with #Sha(B/Q)=kn².

Nous proposons, dans cette thèse, une étude théorique des codes géométriques algébriques construits à partir de surfaces définies sur les corps finis. Nous prouvons des bornes inférieures pour la distance minimale des codes sur des surfaces dont le diviseur canonique est soit nef soit anti-strictement nef et sur des surfaces sans courbes irréductibles de petit genre. Nous améliorons ces bornes inférieures dans le cas des surfaces dont le nombre de Picard arithmétique est égal à un, des surfaces sans courbes de petite auto-intersection et des surfaces fibrées. Ensuite, nous appliquons ces bornes aux surfaces plongées dans P3. Une attention particulière est accordée aux codes construits à partir des surfaces abéliennes. Dans ce contexte, nous donnons une borne générale sur la distance minimale et nous démontrons que cette estimation peut être améliorée en supposant que la surface abélienne ne contient pas de courbes absolument irréductibles de petit genre. Dans cette optique nous caractérisons toutes les surfaces abéliennes qui ne contiennent pas de courbes absolument irréductibles de genre inférieur ou égal à 2. Cette approche nous conduit naturellement à considérer les restrictions de Weil de courbes elliptiques et les surfaces abéliennes qui n'admettent pas de polarisation principale
In this thesis we provide a theoretical study of algebraic geometry codes from surfaces defined over finite fields. We prove lower bounds for the minimum distance of codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irreducible curves of small genus. We sharpen these lower bounds for surfaces whose arithmetic Picard number equals one, surfaces without curves with small self-intersection and fibered surfaces. Then we apply these bounds to surfaces embedded in P3. A special attention is given to codes constructed from abelian surfaces. In this context we give a general bound on the minimum distance and we prove that this estimation can be sharpened under the assumption that the abelian surface does not contain absolutely irreducible curves of small genus. In this perspective we characterize all abelian surfaces which do not contain absolutely irreducible curves of genus up to 2. This approach naturally leads us to consider Weil restrictions of elliptic curves and abelian surfaces which do not admit a principal polarization

L'objectif de cette thèse est l'étude des propriétés concernant la finitude, la croissance, la nonexistence générique et l'uniformité de l'ensemble des sections (S,D)-entières d'une famille des variétés abéliennes A fibrée au-dessus d'une surface de Riemann compacte B. Le sous-ensemble S de B est arbitraire et n'est pas nécessairement fini. Ces sections entières correspondent aux points rationnels de la fibre générique de A et qui ne peuvent intersecter le diviseur D de A qu'au-dessus de S. Dans ce contexte, une machinerie appelée hauteur hyperbolique-homotopique est introduite pour jouer le rôle de la théorie d'intersection. Nous démontrons plusieurs nouveaux résultats sur la finitude de certaines unions larges de sections (S, D)-entières ainsi que leur croissance polynomiale en fonction du cardinal de la restriction de S à un certain ouvert complexe petit U de B. Ces résultats sont hors de portée des méthodes purement algébriques. Ainsi, nos travaux mettent en évidence certains phénomènes nouveaux en faveur de la version géométrique de la conjecture de Lang-Vojta. Si A est une surface elliptique, les mêmes conclusions restent vraies où non seulement S mais D peuvent aussi varier en familles. Nous démontrons également un résultat négatif concernant le théorème de Parshin-Arakelov
We study the finiteness, growth order, generic emptyness, and uniformity of the set of (S,D)-integral sections in an abelian fibration A over a compact Riemann surface B. Here, S is an arbitrary subset of B and not necessarily finite. These integral sections correspond to rational points of the generic fibre of A and which intersect the divisor D only possibly above S. We introduce in this context the so-called hyperbolic-homotopic height as a substitute for the classical intersection theory. We then establish several new results concerning the finiteness of various large unions of (S,D)-integral points and their polynomial growth in terms of the caradinality of the restriction of S in U, where the sets S is required to be finite only in a certain small open subset U of B. Such results are out of reach of a purely algebraic method. Thereby, we give some new evidence and phenomena to the Geometric Lang-Vojta conjecture. When A is an elliptic surface, we obtain the same results for certain unions of (S,D)-integral points, where both S and D are allowed to vary in certain families. A negative finiteness result concerning the Parshin-Arakelov theorem is also given

Le but principal de cette thèse de doctorat est l'étude de l'anneau de cohomologie du complément d'une courbe algébrique réduite dans le plan projectif pondéré complexe dont les composantes irréductibles sont des courbes rationnelles (avec ou sans points singuliers). En particulier, des représentants holomorphes (rationnels) sont obtenus pour les classes de cohomologie. Pour atteindre notre objectif, il est nécessaire de développer une théorie algébrique des courbes sur des surfaces avec des singularités quotient et d'étudier des techniques pour calculer certains invariants particulièrement utiles à travers des Q-résolutions plongées
The main goal of this PhD thesis is the study of the cohomology ring of the complement of a reduced algebraic curve in the complex weighted projective plane whose irreducible components are all rational (possibly singular) curves. In particular, holomorphic (rational) representatives are found for the cohomology classes. In order to achieve our purpose one needs to develop an algebraic theory of curves on surfaces with quotient singularities and study techniques to compute some particularly useful invariants by means of embedded Q-resolutions

Diese Dissertation beschäftigt sich mit asymptotischen Syzygien und Gleichungen Abelscher Varietäten, sowie mit deren Anwendung auf zyklische Überdeckungen von Kurven von Geschlecht zwei. Was asymptotischen Syzygien angeht, zeigen wir für beliebige Geradenbündel auf projektiven Schemata: Wenn die asymptotischen Syzygien von Grad p eines Geradenbündels verschwinden, dann ist das Geradenbündel p-sehr ampel. Darüber hinaus verwenden wir die Bridgeland-King-Reid-Haiman Korrespondenz, um zu zeigen, dass dieses Ergebnis auch umgekehrt wahr ist, wenn es um eine glatte Fläche und kleine p geht. Dies dehnt Ergebnisse von Ein-Lazarsfeld und Ein-Lazarsfeld-Yang aus. Wir verwenden unsere Ergebnisse, um zu untersuchen, wie Syzygien verwendet werden können, um den Grad der Irrationalität einer Varietät zu begrenzen. Ferner, beweisen wir eine Vermutung von Gross and Popescu über Abelsche Flächen, deren Ideal durch Quadriken und Kubiken erzeugt wird. Außerdem verwenden wir die projektive Normalität einer Abelschen Fläche, um die Prym Abbildung, die mit zyklischen Überdeckungen von Geschlecht zwei Kurven assoziert ist, zu untersuchen. Wir zeigen, dass das Differential der Abbildung generisch injektiv ist, wenn der Grad der Überdeckung mindestens sieben ist. Wir dehnen damit Ergebnisse von Lange und Ortega aus. Abschließend zeigen wir, dass das Differential genau für bielliptische Überdeckungen nicht injectiv ist.
In this thesis we study asymptotic syzygies of algebraic varieties and equations of abelian surfaces, with applications to cyclic covers of genus two curves. First, we show that vanishing of asymptotic p-th syzygies implies p-very ampleness for line bundles on arbitrary projective schemes. For smooth surfaces we prove that the converse holds, when p is small, by studying the Bridgeland-King-Reid-Haiman correspondence for the Hilbert scheme of points. This extends previous results of Ein-Lazarsfeld and Ein-Lazarsfeld-Yang. As an application of our results, we show how to use syzygies to bound the irrationality of a variety. Furthermore, we confirm a conjecture of Gross and Popescu about abelian surfaces whose ideal is generated by quadrics and cubics. In addition, we use projective normality of abelian surfaces to study the Prym map associated to cyclic covers of genus two curves. We show that the differential of the map is generically injective as soon as the degree of the cover is at least seven, extending a previous result of Lange and Ortega. Moreover, we show that the differentials fails to be injective precisely at bielliptic covers.

Dans ce travail, nous classifions les automorphismes non-symplectiques des variétés équivalentes par déformations à des variétés de Kummer généralisées de dimension 4, ayant une action d'ordre premier sur le réseau de Beauville-Bogomolov. Dans un premier temps, nous donnons les lieux fixes des automorphismes naturels de cette forme. Par la suite, nous développons des outils sur les réseaux en vue de les appliquer à nos variétés. Une étude réticulaire des tores complexes de dimension 2 permet de mieux comprendre les automorphismes naturels sur les variétés de type Kummer. Nous classifions finalement tous les automorphismes décrits précédemment sur ces variétés. En application de nos résultats sur les réseaux, nous complétons également la classification des automorphismes d'ordre premier sur les variétés équivalentes par déformations à des schémas de Hilbert de 2 points sur des surfaces K3, en traitant le cas de l'ordre 5 qui restait ouvert
Ln this work, we classify non-symplectic automorphisms of varieties deformation equivalent to 4-dimensional generalized Kummer varieties, having a prime order action on the Beauville-Bogomolov lattice. Firstly, we give the fixed loci of natural automorphisms of this kind. Thereafter, we develop tools on lattices, in order to apply them to our varieties. A lattice-theoritic study of 2-dimensional complex tori allows a better understanding of natural automorphisms of Kummer-type varieties. Finaly, we classify all the automorphisms described above on thos varieties. As an application of our results on lattices, we complete also the classification of prime order automorphisms on varieties deformation-equivalent to Hilbert schemes of 2 points on K3 surfaces, solving the case of order 5 which was still open

Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2007.
Title from electronic title page (viewed Dec. 18, 2007). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics." Discipline: Mathematics; Department/School: Mathematics. On t.p., z has n as a superscript.

This thesis studies non-simple Jacobians and non-simple abelian varieties. The moti- vation of the study is a construction which gives a distinguished genus 4 curve in the linear system of a (1, 3)-polarised surface. The main theorem characterises such curves as hyperelliptic genus 4 curves whose Jacobian contains a (1, 3)-polarised surface. This leads to investigating the locus of non-simple principally polarised abelian g- folds. The main theorem of this part shows that the irreducible components of this locus are Is~, defined as the locus of principally polarised g-folds having an abelian subvariety with induced polarisation of type d. = (d1, ... , dk), where k ≤ g/2 Moreover, there are theorems which characterise the Jacobians of curves that are etale double covers or double covers branched in two points. There is also a detailed computation showing that, for p > 1 an odd number, the hyperelliptic locus meets IS4(l,p) transversely in the Siegel upper half space

En ce travail, trois questions liées au cocycle de Kontsevich–Zorich dans l'espaces de modules des différentielles quadratiques sont étudies avec des techniques combinatoires.Les deux premières impliquent la structure des groupes de Rauzy–Veech des différentielles abéliennes et quadratiques, respectivement. Ces groupes encodent l'action homologique des orbites presque fermées du flot géodésique de Teichmüller dans une composante connexe donnée d'une strate via le cocycle de Kontsevich–Zorich. Pour le cas abélien, on classifie complètement ces groupes et on montre qu'ils sont des sous-groupes explicites des groupes symplectiques, et qu'ils sont commensurables avec des réseaux arithmétiques. Pour le cas quadratique, on montre qu'ils sont aussi commensurables avec des réseaux arithmétiques si certaines conditions sur les ordres des singularités sont satisfaites.La troisième question implique la réalisabilité de certain groupes algébriques comme adhérences de Zariski des groupes de monodromie des surfaces à petits carreaux. En fait, on montre que quelques groupes de la forme SO*(2d) sont réalisables comme telles adhérences
In this work, three questions related to the Kontsevich--Zorich cocycle in the moduli space of quadratic differentials are studied by using combinatorial techniques.The first two deal with the structure of the Rauzy--Veech groups of Abelian and quadratic differentials, respectively. These groups encode the homological action of almost-closed orbits of the Teichmüller geodesic flow in a given component of a stratum via the Kontsevich--Zorich cocycle. For Abelian differentials, we completely classify such groups, showing that they are explicit subgroups of symplectic groups that are commensurable to arithmetic lattices. For quadratic differentials, we show that they are also commensurable to arithmetic lattices of symplectic groups if certain conditions on the orders of the singularities are satisfied.The third question deals with the realisability of certain algebraic groups as Zariski-closures of monodromy groups of square-tiled surfaces. Indeed, we show that some groups of the form SO*(2d) are realisable as such Zariski-closures

In this thesis we investigate wall-crossing phenomena in the stability manifold of an irreducible principally polarized abelian surface for objects with the same invariants as (twists of) ideal sheaves of points. In particular, we construct a sequence of fine moduli spaces which are related by Mukai flops and observe that the stability of these objects is completely determined by the configuration of points. Finally, we use Fourier-Mukai theory to show that these moduli are projective.

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Honeybees managed in semi-arid region were observed with the objective to determine the individual body surface temperature in different places, as well the heat loss by convection. The body surface temperature was measured with micro thermocouple type T touching in three different body region (the head, thorax and abdomen), its collected from four different places (beehive, hive entrance, foraging and watering place) in which they was arrested by the wings between thumb and forefinger for a few seconds, without causing any injury to the animal. The same time was made measurements of climatic variables. The convective heat transfer was estimated by the theory of convection from a horizontal cylinder. The results showed that had different among temperature surface in parts of the body and in different places. The thorax showed the hottest part of the body, then the head and abdomen was the coldest. In hive entrance the bee had the highest thorax temperature (36.6°C) due the shivering caused for flight muscles. Already, in watering place the surface temperature was the lowest in all parts of the body probably because almost always the body surface had wet by water, if not, at the time of measuring the bee regurgitated the liquid ingest in your body. When the bee was in beehive and in hive entrance (in conditions of low wind) the heat loss by convection increases from 0 to 7.5 W m-2 while increase in the gradient temperature from 0 to 10ºC, but when the wind was 1.0 ms-1 the heat loss by convection increases from 0 to 27.5 W cm-2. In bee hive when the black globe showed a temperature of 43°C, the body surface temperature of bee was 46°C, but when the black globe temperature increased 6°C, the body surface temperature lowered 3°C. These results clearly explain that the bee in a semi-arid region in individual or society has physiological and behavioral mechanisms to regulate their body temperature, but more studies are requires know the most efficient thermoregulatory processes. And climatic variations of the environment are crucially to their thermoregulatory behavior
Abelhas criadas em uma região semi-árida foram observadas com o objetivo de determinar qual a temperatura da superfície corpórea do individuo em diferentes lugares, além da sua perda de calor por convecção. A temperatura da superfície corporal foi medida com micro-termopar tipo T tocando em três diferentes regiões do corpo (cabeça, tórax e abdome) da abelha, sendo estas coletadas em quatro diferentes lugares: dentro da colméia, no alvado, forrageando e no bebedouro. Para a medição da temperatura da superfície corpórea, as abelhas tinham as asas presas pelo dedo polegar e indicador por alguns segundos e logo após eram soltas, sem causar nenhuma injúria ao animal. Ao mesmo tempo era feitas as medições das variáveis climáticas. A transferência de calor por convecção foi estimada aplicando-se a teoria da convecção em cilindros horizontais. Os resultados mostraram que houve diferença de temperatura de superfície entre as partes do corpo e nos diferentes lugares. O tórax apresentou a parte mais quente do corpo, seguido da cabeça e abdômen. A abelha no alvado apresentou a maior temperatura de superfície do tórax (36,6°C). Já, no bebedouro a temperatura de superfície foi a mais baixa em todas as partes do corpo. Provavelmente por apresentarem quase sempre a superfície do corpo molhada, se não, na hora da medição a abelha regurgitava a água ingerida no seu próprio corpo. Quando a abelha se encontrava dentro da colméia e no alvado a perda de calor por convecção aumentou de 0 a 7,5 W m-2 com o aumento no gradiente de temperatura de 0 a 10ºC, mas quando o vento foi de 1,0 m s-1 a perda de calor por convecção aumentou de 0 a 27,5 W m-2. Quando a abelha estava no interior da colméia e o globo negro apresentou uma temperatura de 43°C, a temperatura de superfície corpórea desta foi de 46°C, mas quando a temperatura de globo negro aumentou 6°C, a temperatura de superfície corporal da abelha baixou 3°C. Estes resultados explicam claramente que as abelhas em uma região semi-árida como indivíduo ou em colônia possuem mecanismos fisiológicos e comportamentais para regular sua temperatura corporal. E que as variações climáticas do meio ambiente são determinantes para o seu comportamento termorregulatório
2017-05-16

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The temperature control in Apis mellifera is realized by the bees themselves through behavioral adjustments in order to keep the temperature at optimum levels. Unfavorable climatic conditions such as high temperatures and intense solar radiation can cause overheating of the colonies and consequently damage to beekeeping. The objective of this work was to evaluate how africanized bees (Apis mellifera L.) control temperature under different conditions, exposed and protected from direct solar radiation in a semiarid environment. Three colonies of Africanized bees housed in Langstroth hives that were changed every 3 months were used, total of twelve colonies. The internal temperatures and humidity of the three colonies were recorded using thermohygrometer. The body surface temperature of the bees was measured in three parts of the bee's body, head, chest and abdomen, using a mini infrared thermometer. Observations of the social behavior of ventilation were classified into four levels ranging from none to high ventilatory activity. When the hives were in the shade the internal temperature of the hives remained within the range considered optimal, while in the sun, this condition was not reached. In the shade, the bees managed to keep the relative humidity stable. In the sun, there was an increase in internal humidity as the bees carried water to the hive in order to lower the internal temperature. The ventilation behavior was much more expressive in hives than in the sun, since in the shade only few bees were recruited for this task. The bees that were in the shade, managed to maintain their body temperatures at relatively normal levels, while the bees that was in the sun, had a considered increase of its temperatures. The chest temperature is the highest, followed by the head and abdomen. The mechanisms of temperature control used at colony level and at individual level in the shade were, low ventilation activity and heat transfer to the head, respectively. In the sun, at colony level were distribution of water in the hive and high activity of ventilation and at the individual level transfer of heat to head and abdomen and use of water to wet the body surface. The results obtained in this work, represent a mean collected data of individuals surface temperature of the bees and data of temperature and humidity inside the hives, which constitute important subsidies for an understanding of three fundamental principles for a beekeeping, or abandonment of the bees In drought, a low productivity in the semi-arid and a need of construction of cans for the supply of shade in the apiaries
O controle de temperatura em Apis mellifera, é realizado pelas próprias abelhas através de ajustes comportamentais de forma a manter a temperatura em níveis ótimos. Condições climáticas desfavoráveis, como altas temperaturas e intensa radiação solar podem causar o superaquecimento das colônias e consequentemente prejuízos para a apicultura. Este trabalho teve como objetivo avaliar como as abelhas africanizadas (Apis mellifera L.) realizam o controle de temperatura, sob duas condições distintas, expostas e protegidas da radiação solar direta em ambiente semiárido. Foram utilizadas três colônias de abelhas africanizadas alojadas em colmeias modelo Langstroth que eram trocadas a cada 3 meses, totalizando doze colônias. Foram registradas as temperaturas e umidades internas das três colônias, utilizando-se um termohigrômetro digital. A temperatura de superfície corpórea das abelhas foi aferida em três partes do corpo da abelha, cabeça, tórax e abdômen, utilizando-se um mini termômetro de infravermelho. As observações do comportamento social de ventilação foi classificada em quatro níveis que variavam de nenhuma, a alta atividade ventilatória. Quando as colmeias estavam na sombra a temperatura interna das colmeias permaneceu dentro da faixa considerada ótima, enquanto ao sol, essa condição não foi alcançada. Na sombra as abelhas conseguiram manter a umidade relativa estável. Já no sol, houve um aumento da umidade interna pois as abelhas levavam agua para a colmeia com o intuito de baixar a temperatura interna. O comportamento de ventilação foi bem mais expressivo nas colmeias que estavam ao sol, já na sombra apenas poucas abelhas eram recrutadas para esta tarefa. As abelhas que estavam na sombra, conseguiram manter suas temperaturas corporais em níveis relativamente normais, enquanto as abelhas que estava ao sol, tiveram um aumento considerado de suas temperaturas. A temperatura do tórax é a mais elevada, seguida da cabeça e do abdômen. Os mecanismos de controle de temperatura utilizados a nível de colônia e em nível individual na sombra foram, baixa atividade de ventilação e transferência de calor para a cabeça, respectivamente. No sol, a nível de colônia foram, distribuição de água na colmeia e alta atividade de ventilação e a nível individual transferência de calor para cabeça e abdômen e utilização de água para molhar a superfície corporal. Os resultados obtidos neste trabalho representa uma significativa coletânea de dados individuais de temperatura de superfície das abelhas e dados de temperatura e umidade no interior das colmeias, que se constituem em importantes subsídios para a compreensão de três aspectos fundamentais para a apicultura, o abandono das abelhas na seca, a baixa produtividade no semiárido e a necessidade de construção de latadas para fornecimento de sombra nos apiários
2017-08-22

Fix an integer d>0. In 2008, Chantal David and Tom Weston showed that, on average, an elliptic curve over Q picks up a nontrivial p-torsion point defined over a finite extension K of the p-adics of degree at most d for only finitely many primes p. This dissertation is an extension of that work, investigating the frequency with which a principally polarized abelian surface A over Q with real multiplication by Q adjoin a squared-root of 5 has a nontrivial p-torsion point defined over K. Averaging by height, the main result shows that A picks up a nontrivial p-torsion point over K for only finitely many p. The proof of our main theorem primarily rests on three lemmas. The first lemma uses the reduction-exact sequence of an abelian surface defined over an unramified extension K of Q p to give a mod p2 condition for detecting when A has a nontrivial p-torsion point defined over K. The second lemma employs crystalline Dieudonné theory to count the number of isomorphism classes of lifts of abelian surfaces over Fp to Z/p2 that satisfy the condition from our first lemma. Finally, the third lemma addresses the issue of the assumption in the first lemma that K is an unramified extension of Qp. Specifically, it shows that if A has a nontrivial p-torsion point over a ramified extension K of Qp and p - 1 > d then this p-torsion point is actually defined over the maximal unramified subextension of K. We then combine these algebraic results to reduce the main analytic calculation to a series of straightforward estimates.

Fix an integer d > 0. In 2008, Chantal David and Tom Weston showed that, on average, an elliptic curve over Q picks up a nontrivial p-torsion point defined over a finite extension K of the p-adics of degree at most d for only finitely many primes p. This dissertation is an extension of that work, investigating the frequency with which a principally polarized abelian surface A over Q with real multiplication by Q adjoin a squared-root of 5 has a nontrivial p-torsion point defined over K. Averaging by height, the main result shows that A picks up a nontrivial p-torsion point over K for only finitely many p. The proof of our main theorem primarily rests on three lemmas. The first lemma uses the reduction-exact sequence of an abelian survace defined over an unramified extension K of Qp to give a mod p2 condition for detecting when A has a nontrival p-torsion point defined over K. The second lemma employs crystalline Dieudonne theory to count the number of isomorphism classes of lifts of abelian surfaces over Fp to Z/pp that satisfy the conditions from our first lemma. Finally, the third lemma addresses the issue of the assumption in the first lemma that K is an unramified extension of Qp. Specifically, it shows that if A has a nontrival p-torsion point over a ramified extension K of Qp and p - 1 > d then this p-torsion point is actually defined over the maximal unramified subextension of K. We then combine these algebraic results to reduce the main analytic calculation toa series of straightforward estimates.

Thesis (Ph. D.)--Florida State University, 2004.
Advisor: Dr. Wolfgang Heil, Florida State University, College of Arts and Sciences, Dept. of Mathematics. Title and description from dissertation home page (viewed Sept. 28, 2004). Includes bibliographical references.