Dissertations / Theses on the topic 'Birational geometry of surfaces'
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Barros, Ignacio. "K3 surfaces and moduli of holomorphic differentials." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19290.
Full textIn this thesis we investigate the birational geometry of various moduli spaces; moduli spaces of curves together with a k-differential of prescribed vanishing, best known as strata of differentials, moduli spaces of K3 surfaces with marked points, and moduli spaces of curves. For particular genera, we give estimates for the Kodaira dimension, construct unirational parameterizations, rational covering curves, and different birational models. In Chapter 1 we introduce the objects of study and give a broad brush stroke about their most important known features and open problems. In Chapter 2 we construct an auxiliary moduli space that serves as a bridge between certain finite quotients of Mgn for small g and the moduli space of polarized K3 surfaces of genus eleven. We develop the deformation theory necessary to study properties of the mentioned moduli space. In Chapter 3 we use this machinery to construct birational models for the moduli spaces of polarized K3 surfaces of genus eleven with marked points and we use this to conclude results about the Kodaira dimension. We prove that the moduli space of polarized K3 surfaces of genus eleven with n marked points is unirational when n<= 6 and uniruled when n<=7. We also prove that the moduli space of polarized K3 surfaces of genus eleven with n marked points has non-negative Kodaira dimension for n>= 9. In the final section, we make a connection with some of the missing cases in the Kodaira classification of Mgnbar. Finally, in Chapter 4 we address the question concerning the birational geometry of strata of holomorphic and quadratic differentials. We show strata of holomorphic and quadratic differentials to be uniruled in small genus by constructing rational curves via pencils on K3 and del Pezzo surfaces respectively. Restricting to genus 3<= g<=6 we construct projective bundles over rational varieties that dominate the holomorphic strata with length at most g-1, hence showing in addition, these strata are unirational.
Beri, Pietro. "On birational transformations and automorphisms of some hyperkähler manifolds." Thesis, Poitiers, 2020. http://www.theses.fr/2020POIT2267.
Full textMy thesis work focuses on double EPW sextics, a family of hyperkähler manifolds which, in the general case, are equivalent by deformation to Hilbert's scheme of two points on a K3 surface. In particular I used the link that these manifolds have with Gushel-Mukai varieties, which are Fano varieties in a Grassmannian if their dimension is greater than two, K3 surfaces if their dimension is two.The first chapter contains some reminders of the theory of Pell's equations and lattices, which are fundamental for the study of hyperkähler manifolds. Then I recall the construction which associates a double covering to a sheaf on a normal variety.In the second chapter I discuss hyperkähler manifolds and describe their first properties; I also introduce the first case of hyperkähler manifold that has been studied, the K3 surfaces. This family of surfaces corresponds to the hyperkähler manifolds in dimension two.Furthermore, I briefly present some of the latest results in this field, in particular I define different module spaces of hyperkähler manifolds, and I describe the action of automorphism on the second cohomology group of a hyperkähler manifold.The tools introduced in the previous chapter do not provide a geometrical description of the action of automorphism on the manifold for the case of the Hilbert scheme of points on a general K3 surface. In the third chapter, I therefore introduce a geometrical description up to a certain deformation. This deformation takes into account the structure of Hilbert scheme. To do so, I introduce an isomorphism between a connected component of the module space of manifolds of type K3[n] with a polarization, and the module space of manifolds of the same type with an involution of which the rank of the invariant is one. This is a generalization of a result obtained by Boissière, An. Cattaneo, Markushevich and Sarti in dimension two. The first two parts of this chapter are a joint work with Alberto Cattaneo.In the fourth chapter, I define EPW sextics, using O'Grady's argument, which shows that a double covering of a EPW sextic in the general case is deformation equivalent to the Hilbert square of a K3 surface. Next, I present the Gushel-Mukai varieties, with emphasis on their connection with EPW sextics; this approach was introduced by O'Grady, continued by Iliev and Manivel and systematized by Kuznetsov and Debarre.In the fifth chapter, I use the tools introduced in the fourth chapter in the case where a K3 surface can be associated to a EPW sextic X. In this case I give explicit conditions on the Picard group of the surface for X to be a hyperkähler manifold. This allows to use Torelli's theorem for a K3 surface to demonstrate the existence of some automorphisms on X. I give some bounds on the structure of a subgroup of automorphisms of a sextic EPW under conditions of existence of a fixed point for the action of the group.Still in the case of the existence of a K3 surface associated with a EPW sextic X, I improve the bound obtained previously on the automorphisms of X, by giving an explicit link with the number of conics on the K3 surface. I show that the symplecticity of an automorphism on X depends on the symplecticity of a corresponding automorphism on the surface K3.The sixth chapter is a work in collaboration with Alberto Cattaneo. I study the group of birational automorphisms on Hilbert's scheme of points on a projective surface K3, in the generic case. This generalizes the result obtained in dimension two by Debarre and Macrì. Then I study the cases where there is a birational model where these automorphisms are regular. I describe in a geometrical way some involutions, whose existence has been proved before
Fanelli, Andrea. "Two structural aspects in birational geometry : geography of Mori fibre spaces and Matsusaka's theorem for surfaces in positive characteristic." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/26285.
Full textBenzerga, Mohamed. "Structures réelles sur les surfaces rationnelles." Thesis, Angers, 2016. http://www.theses.fr/2016ANGE0081.
Full textThe aim of this PhD thesis is to give a partial answer to the finiteness problem for R-isomorphism classes of real forms of any smooth projective complex rational surface X, i.e. for the isomorphism classes of R-schemes whose complexification is isomorphic to X. We study this problem in terms of real structures (or antiholomorphic involutions, which generalize complex conjugation) on X: the advantage of this approach is that it helps us rephrasing our problem with automorphism groups of rational surfaces, via Galois cohomology. Thanks to recent results on these automorphism groups, using hyperbolic geometry and, to a lesser extent, holomorphic dynamics and metric geometry, we prove several finiteness results which go further than Del Pezzo surfaces and can apply to some rational surfaces with large automorphism groups
Boitrel, Aurore. "Groupes d'automorphismes des surfaces del Pezzo sur un corps parfait." Electronic Thesis or Diss., université Paris-Saclay, 2025. http://www.theses.fr/2025UPASM002.
Full textDel Pezzo surfaces are algebraic surfaces with quite special properties, that play an importantpart in the classification of projective algebraic surfaces up to birational transformations.The classification of smooth rational del Pezzo surfaces of degree d over an arbitraryperfect field is classical for d = 7, 8, 9 and new for d = 6. The same is the case for thedescription of their groups of automorphisms. Their classification and the description of theirautomorphism groups is much more difficult for d ≤ 5, as one can see already if the groundfield is the field of real numbers, and the classification is open over a general perfect field.Partial classifications exist over finite fields. Accordingly, we do not know their automorphismgroups in general.The objective of the thesis is to classify the smooth rational del Pezzo surfaces of degreed = 5 and d = 4 over an arbitrary perfect field and describe their automorphism groups.Due to the difficulty of the project, the case d = 4 will only be studied over the field ofreal numbers
Krylov, Igor. "Birational geometry of Fano fibrations." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/28857.
Full textDURIGHETTO, Sara. "Classical and Derived Birational Geometry." Doctoral thesis, Università degli studi di Ferrara, 2019. http://hdl.handle.net/11392/2488324.
Full textNell'ambito della geometria algebrica, lo studio delle trasformazioni birazionali e delle loro proprietà riveste un ruolo di importanza primaria. In questo, si affiancano l'approccio classico della scuola italiana che si concentra sul gruppo di Cremona e quello più moderno che utilizza strumenti come categorie derivate e decomposizioni semiortogonali. Del gruppo di Cremona Cr_n, cioé il gruppo degli automorfismi birazionali di P^n, in generale non si conosce molto e ci si concentra sul caso complesso. Si conosce un insieme di generatori solo nel caso di dimensione 2. Inoltre non é ancora nota una classicazione tramite trasformazioni di Cremona delle curve e dei sistemi lineari di P^2. Tra i casi noti ci sono: le curve irriducibili e quelle formate da due componenti irriducibili. In questa tesi ci si approccia al caso di una configurazione di d rette nel piano proiettivo. Il teorema finale fornisce condizioni necessarie o sufficienti alla contraibilità. Da un punto di vista categoriale invece, le decomposizioni semiortogonali della cat- egoria derivata di una varietà ci forniscono degli invarianti utili nello studio della varietà. Seguendo l'approccio di Clemens-Griffiths riguardante la cubica complessa di dimensione 3, si vuole caratterizzare le ostruzioni alla razionalità di una varietà X di dimensione n. L'idea è di raccogliere le componenti di una decomposizione ortog- onale che non sono equivalenti a categorie derivate di varietà di dimensione almeno n-1 e in questo modo definire quella che chiamiamo componente di Griffiths- Kuznetsov di X. In questa tesi si studia il caso delle superci geometricamante razionali su un campo arbitrario, si definisce tale componente e si mostra che essa è un invariante birazionale. Si vede anche che la componente di Griffiths-Kuznetsov è nulla solo se la supercie è razionale.
Zong, Hong R. "Topics in birational geometry of algebraic varieties." Thesis, Princeton University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3665359.
Full textVarious questions related to birational properties of algebraic varieties are concerned.
Rationally connected varieties are recognized as the buildings blocks of all varieties by the Minimal Model theory. We prove that every curve on a separably rationally connected variety is rationally equivalent to a (non-effective) integral sum of rational curves. That is, the Chow group of 1-cycles is generated by rational curves. As a consequence, we solve a question of Professor Burt Totaro on integral Hodge classes on rationally connected 3-folds. And by a result of Professor Claire Voisin, the general case will be a consequence of the Tate conjecture for surfaces over finite fields.
Using the same philosophy looking for degenerated rational components through forgetful maps between moduli spaces of curves, we prove Weak Approximation conjecture to Prof. Hassett and Prof. Tschinkel for isotrivial families of rationally connected varieties. Theory of Twisted Stable maps is essentially used, with an alternative proof where some notion from Derived Algebraic Geometry is applied. It is remarkable that technics and ideas developed in this part, shed light upon and essentially led to the final solution to weak approximation of Cubic Surfaces, which is a problem concerned by Number Theorists for many years, and this is currently the best known result in this subject.
Then we turn to Minimal Model theory in both zero and positive characteristics. Firstly, projective globally F-regular threefolds of characteristic p ≥ 11, are shown to be rationally chain connected, and back to characteristic zero, we use hard-core technics of Minimal Model program, esp. finite generate of canonical rings due to Professor Hacon, Professor McKernan et al. to characterize Toric varieties and geometric rational varieties as log canonical log-Calabi Yau varieties with "large" boundary, where the specific meanings of "large" are originated from some notion of "charges" from String theory, and hence is related to Mirror Symmetry. This part of works also answered a Conjecture due to Prof. Shokurov.
Rulla, William Frederick. "The birational geometry of M₃ and M₂, ₁ /." Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3008434.
Full textMassarenti, Alex. "Biregular and Birational Geometry of Algebraic Varieties." Doctoral thesis, SISSA, 2013. http://hdl.handle.net/20.500.11767/4679.
Full textJohnstone, E. "On the birational geometry of singular Fano varieties." Thesis, University of Liverpool, 2017. http://livrepository.liverpool.ac.uk/3008126/.
Full textTyler, Michael Peter. "On the birational section conjecture over function fields." Thesis, University of Exeter, 2017. http://hdl.handle.net/10871/31600.
Full textDaigle, Daniel. "Birational endomorphisms of the affine plane." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75337.
Full textA graph-theoretic machinery is developed to keep track of the desingularization of the divisors at infinity of the plane. That machinery is then used to investigate the problem of classifying all birational endomorphisms of the plane, and a complete classification is given in the case of two fundamental points.
Farkas, Gavril Marius. "The birational geometry of the moduli space of curves." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2000. http://dare.uva.nl/document/84192.
Full textPerry, Alexander Richard. "Derived categories and birational geometry of Gushel-Mukai varieties." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493330.
Full textMathematics
Krashen, Daniel Reuben. "Birational isomorphisms between Severi-Brauer varieties." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3034558.
Full textKaloghiros, Anne-Sophie. "The topology of terminal quartic 3-folds." Thesis, University of Cambridge, 2007. https://www.repository.cam.ac.uk/handle/1810/214794.
Full textVenkatram, Kartik (Kartik Swaminathan). "Birational geometry of the space of rational curves in homogeneous varieties." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/68484.
Full textCataloged from PDF version of thesis.
Includes bibliographical references (p. 55-56).
In this thesis, we investigate the birational geometry of the space of rational curves in various homogeneous spaces, with a focus on the quasi-map compactification induced by the Quot and Hyperquot functors. We first study the birational geometry of the Quot scheme of sheaves on P1 via techniques from the Mori program, explicitly describing its associated cones of ample and effective divisors as well as the various Mori chambers within the latter. We compute the base loci of all effective divisors, and give a conjectural description of the induced birational models. We then partially extend our results to the Hyperquot scheme of sheaves on P', which gives the analogous compactification for rational curves in flag varieties. We fully describe the cone of ample divisors in all cases and the cone of effective divisors in certain ones, but only claim a partial description of the latter in general.
by Kartik Venkatram.
Ph.D.
Duran, James Joseph. "Differential geometry of surfaces and minimal surfaces." CSUSB ScholarWorks, 1997. https://scholarworks.lib.csusb.edu/etd-project/1542.
Full textAghasi, Mansour. "Geometry of arithmetic surfaces." Thesis, Durham University, 1996. http://etheses.dur.ac.uk/5270/.
Full textChaparro, Maria Guadalupe. "Minimal surfaces." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3118.
Full textMboro, René. "Birational invariants : cohomology, algebraic cycles and Hodge theory cohomologie." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX049/document.
Full textIn this thesis, we study some birational invariants of smooth projective varieties, in view of rationality questions for these varieties. It consists of three parts, that can be read independently.In the first chapter, we study, for some families of varieties, some stable birational invariants, that vanish for projective space and that appear naturally with Manin formulas. On one hand, we show for complex cubic 5-folds that the birational invariant given by the group of torsion codimension 3 cycles annihilated by the Deligne cycle map is controlled by the group of torsion 1-cycles of its variety of lines annihilated by the Deligne cycle map. We also prove that the Griffiths group of 1-cycles for the variety of lines of a hypersurface of the projective space over an algebraically closed field of characteristic 0, is trivial when the variety is smooth and Fano of index at least 3.The two last chapters focus on different aspects of the Chow-theoretic decomposition of the diagonal, a property which is invariant under stable birational equivalence, recently introduced by Voisin. In the second chapter, we adapt in characteristic greater than 2, part of the results, obtained by Voisin over the complex numbers, on the decomposition of the diagonal of cubic threefolds.In the last chapter, we study the concept of essential CH_0-dimension introduced by Voisin and related to the decomposition of the diagonal in that having essential CH_0-dimension 0 is equivalent to admitting a Chow-theoretic decomposition of the diagonal. We give sufficient (and necessary) conditions, for a complex variety with trivial group of 0-cycles, having essential CH_0-dimension non greater than 2 to admit a Chow-theoretic decomposition of the diagonal
Syzdek, Wioletta. "Seshadri constants and geometry of surfaces." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975820532.
Full textMitsui, Kentaro. "Bimeromorphic geometry of rigid analytic surfaces." 京都大学 (Kyoto University), 2011. http://hdl.handle.net/2433/142438.
Full textHe, Zhuang. "On Moduli Spaces of Weighted Pointed Stable Curves and Applications." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1437187765.
Full textBråmå, Erik. "Strain Energy of Bézier Surfaces." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-145645.
Full textO'Neill, Edward Finbar. "Geometry based constructions for curves and surfaces." Thesis, University of Birmingham, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.251132.
Full textDangskul, Supreedee. "Construction of Seifert surfaces by differential geometry." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20382.
Full textKaba, Mustafa Devrim. "On The Arithmetic Of Fibered Surfaces." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613674/index.pdf.
Full texts conjectures, for a certain class of algebraic surfaces. The surfaces we are interested in are assumed to be defined over a number field, have irregularity two and admit a genus two fibration over an elliptic curve. In the final chapter of the thesis we prove the isomorphism of the Picard motives of an arbitrary variety and its Albanese variety.
Liu, Yang. "Optimization and differential geometry for geometric modeling." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B40988077.
Full textBerardini, Elena. "Algebraic geometry codes from surfaces over finite fields." Thesis, Aix-Marseille, 2020. http://www.theses.fr/2020AIXM0170.
Full textIn 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
Corman, Etienne. "Functional representation of deformable surfaces for geometry processing." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX075/document.
Full textCreating and understanding deformations of surfaces is a recurring theme in geometry processing. As smooth surfaces can be represented in many ways from point clouds to triangle meshes, one of the challenges is being able to compare or deform consistently discrete shapes independently of their representation. A possible answer is choosing a flexible representation of deformable surfaces that can easily be transported from one structure to another.Toward this goal, the functional map framework proposes to represent maps between surfaces and, to further extents, deformation of surfaces as operators acting on functions. This approach has been recently introduced in geometry processing but has been extensively used in other fields such as differential geometry, operator theory and dynamical systems, to name just a few. The major advantage of such point of view is to deflect challenging problems, such as shape matching and deformation transfer, toward functional analysis whose discretization has been well studied in various cases. This thesis investigates further analysis and novel applications in this framework. Two aspects of the functional representation framework are discussed.First, given two surfaces, we analyze the underlying deformation. One way to do so is by finding correspondences that minimize the global distortion. To complete the analysis we identify the least and most reliable parts of the mapping by a learning procedure. Once spotted, the flaws in the map can be repaired in a smooth way using a consistent representation of tangent vector fields.The second development concerns the reverse problem: given a deformation represented as an operator how to deform a surface accordingly? In a first approach, we analyse a coordinate-free encoding of the intrinsic and extrinsic structure of a surface as functional operator. In this framework a deformed shape can be recovered up to rigid motion by solving a set of convex optimization problems. Second, we consider a linearized version of the previous method enabling us to understand deformation fields as acting on the underlying metric. This allows us to solve challenging problems such as deformation transfer are solved using simple linear systems of equations
Cox, Anna Lee. "A categorization of piecewise-linear surfaces." Virtual Press, 1994. http://liblink.bsu.edu/uhtbin/catkey/902464.
Full textDepartment of Mathematical Sciences
Deopurkar, Anand. "Alternate Compactifications of Hurwitz Spaces." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10308.
Full textMathematics
Rockwood, A. P. "Blending surfaces in solid geometric modelling." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234923.
Full textMcKinnon, David N. R. "The multiple view geometry of implicit curves and surfaces /." [St. Lucia, Qld.], 2006. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe19677.pdf.
Full textBjörklund, Johan. "Knots and Surfaces in Real Algebraic and Contact Geometry." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-156908.
Full textRandecker, Anja [Verfasser]. "Geometry and topology of wild translation surfaces / Anja Randecker." Karlsruhe : KIT-Bibliothek, 2015. http://d-nb.info/1084112442/34.
Full textYilmaz, Oguzhan. "Repair of complex geometry components and free-form surfaces." Thesis, University of Nottingham, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.437089.
Full textRuffoni, Lorenzo <1989>. "The Geometry of Branched Complex Projective Structures on Surfaces." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amsdottorato.unibo.it/7860/1/ruffoni_lorenzo_tesi.pdf.
Full textLiu, Yang, and 劉洋. "Optimization and differential geometry for geometric modeling." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40988077.
Full textChiek, Veasna. "Geodesic on surfaces of constant Gaussian curvature." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3045.
Full textKotschick, Dieter. "On the geometry of certain 4 - manifolds." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236179.
Full textTurowski, Gudrun. "Nichtparametrische Minimalflächen vom Typ des Kreisrings und ihr Verhalten längs Kanten der Stützfläche." Bonn : [s.n.], 1998. http://catalog.hathitrust.org/api/volumes/oclc/41464677.html.
Full textHuang, Hui. "Efficient reconstruction of 2D images and 3D surfaces." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/2821.
Full textRycroft, Jeanette Erica. "A geometrical investigation into the projections of surfaces and space curves." Thesis, University of Liverpool, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.322492.
Full textGinebre, Emmanuel. "Geometry-dependence of the adhesive strength of biomimetic, micropatterned surfaces." Thesis, Linköpings universitet, Mekanik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-81067.
Full textSánchez, Luis Florial Espinoza. "Surfaces in 4-space from the affine differential geometry viewpoint." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-23032015-142340/.
Full textNesta tese estudamos as superfícies localmente estritamente convexas desde o ponto de vista da geometria diferencial afim e generalizamos algumas ferramentas para subvariedades localmente estritamente convexas de codimensão 2. Introduzimos uma família de métricas afins sobre uma superfície localmente estritamente convexa M no 4-espaço afim. Então, definimos os planos equiafins simétrico e antissimétrico associados com alguma métrica. Mostramos que se M é imersa em uma hiperquádrica localmente estritamente convexa, então os planos simétrico e assimétrico são iguais e contêm o campo vetorial normal afim à hiperquádrica. Em particular, qualquer superfície imersa em uma hiperquádrica localmente estritamente convexa é semiumbílica afim com relação ao plano equiafim simétrico ou antissimétrico. Mais geralmente, usando a métrica do campo transversal sobre M introduzimos o plano normal afim e as famílias de funções distância e altura afim sobre M. Provamos que as singularidades da família de funções altura afim aparecem como direções do plano normal afim e as singularidades da família de funções distância afim aparecem como pontos sobre o plano normal afim e os pontos focais correspondem às singularidades degeneradas da família de funções distância afim. Também provamos que se M é uma superfície imersa em uma hipersuperfície localmente estritamente convexa, então o plano normal afim contém o vetor normal afim à hipersuperfície. Finalmente, concluímos que qualquer superfície imersa em uma hiperesfera localmente estritamente convexa é semiumbílica afim.
Alagal, Wafa Abdullah. "Application of Bridgeland stability to the geometry of abelian surfaces." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20440.
Full textBozhkov, Yuri Dimitrov. "Specific complex geometry of certain complex surfaces and three-folds." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/110781/.
Full text