Relevant bibliographies by topics / Surfaces del Pezzo

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Surfaces del Pezzo'

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Published: 8 March 2025

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Journal articles on the topic "Surfaces del Pezzo"

1

Park, Jihun, and Joonyeong Won. "Log canonical thresholds on Gorenstein canonical del Pezzo surfaces." Proceedings of the Edinburgh Mathematical Society 54, no. 1 (October 28, 2010): 187–219. http://dx.doi.org/10.1017/s001309150900039x.

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AbstractWe classify all the effective anticanonical divisors on weak del Pezzo surfaces. Through this classification we obtain the smallest number among the log canonical thresholds of effective anticanonical divisors on a given Gorenstein canonical del Pezzo surface.
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LUBBES, NIELS. "ALGORITHMS FOR SINGULARITIES AND REAL STRUCTURES OF WEAK DEL PEZZO SURFACES." Journal of Algebra and Its Applications 13, no. 05 (February 25, 2014): 1350158. http://dx.doi.org/10.1142/s0219498813501582.

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In this paper, we consider the classification of singularities [P. Du Val, On isolated singularities of surfaces which do not affect the conditions of adjunction. I, II, III, Proc. Camb. Philos. Soc.30 (1934) 453–491] and real structures [C. T. C. Wall, Real forms of smooth del Pezzo surfaces, J. Reine Angew. Math.1987(375/376) (1987) 47–66, ISSN 0075-4102] of weak Del Pezzo surfaces from an algorithmic point of view. It is well-known that the singularities of weak Del Pezzo surfaces correspond to root subsystems. We present an algorithm which computes the classification of these root subsystems. We represent equivalence classes of root subsystems by unique labels. These labels allow us to construct examples of weak Del Pezzo surfaces with the corresponding singularity configuration. Equivalence classes of real structures of weak Del Pezzo surfaces are also represented by root subsystems. We present an algorithm which computes the classification of real structures. This leads to an alternative proof of the known classification for Del Pezzo surfaces and extends this classification to singular weak Del Pezzo surfaces. As an application we classify families of real conics on cyclides.
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Mehran, Afsaneh. "Kummer surfaces associated to (1, 2)-polarized abelian surfaces." Nagoya Mathematical Journal 202 (June 2011): 127–43. http://dx.doi.org/10.1215/00277630-1260477.

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AbstractThe aim of this paper is to describe the geometry of the generic Kummer surface associated to a (1, 2)-polarized abelian surface. We show that it is the double cover of a weak del Pezzo surface and that it inherits from the del Pezzo surface an interesting elliptic fibration with twelve singular fibers of type I2.
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Mehran, Afsaneh. "Kummer surfaces associated to (1, 2)-polarized abelian surfaces." Nagoya Mathematical Journal 202 (June 2011): 127–43. http://dx.doi.org/10.1017/s002776300001028x.

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AbstractThe aim of this paper is to describe the geometry of the generic Kummer surface associated to a (1, 2)-polarized abelian surface. We show that it is the double cover of a weak del Pezzo surface and that it inherits from the del Pezzo surface an interesting elliptic fibration with twelve singular fibers of typeI2.
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Cascini, Paolo, Hiromu Tanaka, and Jakub Witaszek. "On log del Pezzo surfaces in large characteristic." Compositio Mathematica 153, no. 4 (March 8, 2017): 820–50. http://dx.doi.org/10.1112/s0010437x16008265.

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We show that any Kawamata log terminal del Pezzo surface over an algebraically closed field of large characteristic is globally $F$-regular or it admits a log resolution which lifts to characteristic zero. As a consequence, we prove the Kawamata–Viehweg vanishing theorem for klt del Pezzo surfaces of large characteristic.
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JIANG, CHEN. "BOUNDING THE VOLUMES OF SINGULAR WEAK LOG DEL PEZZO SURFACES." International Journal of Mathematics 24, no. 13 (December 2013): 1350110. http://dx.doi.org/10.1142/s0129167x13501103.

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We give an optimal upper bound for the anti-canonical volume of an ϵ-lc weak log del Pezzo surface. Moreover, we consider the relation between the bound of the volume and the Picard number of the minimal resolution of the surface. Furthermore, we consider blowing up several points on a Hirzebruch surface in general position and give some examples of smooth weak log del Pezzo surfaces.
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Kim, In-Kyun, and Joonyeong Won. "Weakly exceptional singularities of log del Pezzo surfaces." International Journal of Mathematics 30, no. 01 (January 2019): 1950010. http://dx.doi.org/10.1142/s0129167x19500101.

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We complete the computation of global log canonical thresholds, or equivalently alpha invariants, of quasi-smooth well-formed complete intersection log del Pezzo surfaces of amplitude 1 in weighted projective spaces. As an application, we prove that they are weakly exceptional. And we investigate the super-rigid affine Fano 3-folds containing a log del Pezzo surface as boundary.
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Reid, Miles. "Nonnormal del Pezzo surfaces." Publications of the Research Institute for Mathematical Sciences 30, no. 5 (1994): 695–727. http://dx.doi.org/10.2977/prims/1195165581.

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Kuznetsov, Alexander Gennad'evich, and Yuri Gennadievich Prokhorov. "On higher-dimensional del Pezzo varieties." Izvestiya: Mathematics 87, no. 3 (2023): 488–561. http://dx.doi.org/10.4213/im9385e.

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We study del Pezzo varieties, higher-dimensional analogues of del Pezzo surfaces. In particular, we introduce ADE classification of del Pezzo varieties, show that in type $\mathrm A$ the dimension of non-conical del Pezzo varieties is bounded by $12 - d - r$, where $d$ is the degree and $r$ is the rank of the class group, and classify maximal del Pezzo varieties.
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Trepalin, Andrey. "Quotients of del Pezzo surfaces." International Journal of Mathematics 30, no. 12 (November 2019): 1950068. http://dx.doi.org/10.1142/s0129167x1950068x.

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Let [Formula: see text] be any field of characteristic zero, [Formula: see text] be a del Pezzo surface and [Formula: see text] be a finite subgroup in [Formula: see text]. In this paper, we study when the quotient surface [Formula: see text] can be non-rational over [Formula: see text]. Obviously, if there are no smooth [Formula: see text]-points on [Formula: see text] then it is not [Formula: see text]-rational. Therefore, under assumption that the set of smooth [Formula: see text]-points on [Formula: see text] is not empty we show that there are few possibilities for non-[Formula: see text]-rational quotients. The quotients of del Pezzo surfaces of degree [Formula: see text] and greater are considered in the author’s previous papers. In this paper, we study the quotients of del Pezzo surfaces of degree [Formula: see text]. We show that they can be non-[Formula: see text]-rational only for the trivial group or cyclic groups of order [Formula: see text], [Formula: see text] and [Formula: see text]. For the trivial group and the group of order [Formula: see text], we show that both [Formula: see text] and [Formula: see text] are not [Formula: see text]-rational if the [Formula: see text]-invariant Picard number of [Formula: see text] is [Formula: see text]. For the groups of order [Formula: see text] and [Formula: see text], we construct examples of both [Formula: see text]-rational and non-[Formula: see text]-rational quotients of both [Formula: see text]-rational and non-[Formula: see text]-rational del Pezzo surfaces of degree [Formula: see text] such that the [Formula: see text]-invariant Picard number of [Formula: see text] is [Formula: see text]. As a result of complete classification of non-[Formula: see text]-rational quotients of del Pezzo surfaces we classify surfaces that are birationally equivalent to quotients of [Formula: see text]-rational surfaces, and obtain some corollaries concerning fields of invariants of [Formula: see text].
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Dissertations / Theses on the topic "Surfaces del Pezzo"

1

Wilson, Andrew. "Smooth exceptional del Pezzo surfaces." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4735.

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For a Fano variety V with at most Kawamata log terminal (klt) singularities and a finite group G acting bi-regularly on V , we say that V is G-exceptional (resp., G-weakly-exceptional) if the log pair (V,∆) is klt (resp., log canonical) for all G-invariant effective Q-divisors ∆ numerically equivalent to the anti-canonical divisor of V. Such G-exceptional klt Fano varieties V are conjectured to lie in finitely many families by Shokurov ([Sho00, Pro01]). The only cases for which the conjecture is known to hold true are when the dimension of V is one, two, or V is isomorphic to n-dimensional projective space for some n. For the latter, it can be shown that G must be primitive—which implies, in particular, that there exist only finitely many such G (up to conjugation) by a theorem of Jordan ([Pro00]). Smooth G-weakly-exceptional Fano varieties play an important role in non-rationality problems in birational geometry. From the work of Demailly (see [CS08, Appendix A]) it follows that Tian’s αG-invariant for such varieties is no smaller than one, and by a theorem of Tian such varieties admit G-invariant Kähler-Einstein metrics. Moreover, for a smooth G-exceptional Fano variety and given any G-invariant Kähler formin the first Chern class, the Kähler-Ricci iteration converges exponentially fast to the Kähler form associated to a Kähler- Einsteinmetric in the C∞(V)-topology. The termexceptional is inherited from singularity theory, to which this study enjoys strong links. We classify two-dimensional smooth G-exceptional Fano varieties (del Pezzo surfaces) and provide a partial list of all G-exceptional and G-weakly-exceptional pairs (S,G), where S is a smooth del Pezzo surface and G is a finite group of automorphisms of S. Our classification confirms many conjectures on two-dimensional smooth exceptional Fano varieties.
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Loughran, Daniel Thomas. "Manin's conjecture for del Pezzo surfaces." Thesis, University of Bristol, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.544344.

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Kosta, Dimitra. "Del Pezzo surfaces with Du Val singularities." Thesis, University of Edinburgh, 2009. http://hdl.handle.net/1842/3934.

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A lot of attention has been drawn recently to global log canonical thresholds of Fano varieties, which are algebraic counterparts of the α-invariant of Tian for smooth Fano varieties. In particular, global log canonical thresholds are related to the existence of Kahler-Einstein metrics on Fano varieties. The purpose of this thesis is to apply techniques from singularity theory in order to compute the global log canonical thresholds of all Del Pezzo surfaces of degree 1 with Du Val singularities, as well as the global log canonical thresholds of all Del Pezzo surfaces of Picard rank 1 with Du Val singularities. As a consequence, it is proven that Del Pezzo surfaces of degree 1 with Du Val singularities admit a Kahler-Einstein metric if the singular locus consists of only A1, or A3, or A4 type Du Val singular points.
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Ueda, Kazushi. "Homological mirror symmetry for toric del Pezzo surfaces." 京都大学 (Kyoto University), 2006. http://hdl.handle.net/2433/144153.

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Kyoto University (京都大学)
0048
新制・課程博士
博士(理学)
甲第12069号
理博第2963号
新制||理||1443(附属図書館)
23905
UT51-2006-J64
京都大学大学院理学研究科数学・数理解析専攻
(主査)助教授 河合 俊哉, 教授 齋藤 恭司, 教授 柏原 正樹
学位規則第4条第1項該当
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Manzaroli, Matilde. "Real algebraic curves in real del Pezzo surfaces." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLX017/document.

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L’étude topologique des variétés algébriques réelles remonte au moins aux travaux de Harnack, Klein, et Hilbert au 19éme siecle; en particulier, la classification des types d’isotopie réalisés par les courbes algébriques réelles d’un degré fixé dans RP2 est un sujet qui a connu un essor considérable jusqu'à aujourd'hui. En revanche, en dehors des études concernants les surfaces de Hirzebruch et les surfaces de degré au plus 3 dans RP3, à peu près rien n’est connu dans le cas de surfaces ambiantes plus générales. Cela est du en particulier au fait que les variétés construites en utilisant le "patchwork" sont des hypersurfaces de variétés toriques. Or, il existe de nombreuses autre surfaces algébriques réelles. Parmi celles-ci se trouvent les surfaces rationnelles réelles, et plus particulièrement les surfaces rèelles minimales. Dans cette thèse, on élargit l’étude des types d’isotopie réalisés par les courbes algébriques réelles aux surfaces réelles minimales de del Pezzo de degré 1 et 2. En outre, on termine la classification des types topologiques réalisés par les courbes algébriques réelles séparantes et non-séparantes de bidegré (5,5) sur la quadrique ellipsoide
The study of the topology of real algebraic varieties dates back to the work of Harnack, Klein and Hilbert in the 19th century; in particular, the isotopy type classification of real algebraic curves with a fixed degree in RP2 is a classical subject that has undergone considerable evolution. On the other hand, apart from studies concerning Hirzebruch surfaces and at most degree 3 surfaces in RP3, not much is known for more general ambient surfaces. In particular, this is because varieties constructed using the patchworking method are hypersurfaces of toric varieties. However, there are many other real algebraic surfaces. Among these are the real rational surfaces, and more particularly the $mathbb{R}$-minimal surfaces. In this thesis, we extend the study of the topological types realized by real algebraic curves to the real minimal del Pezzo surfaces of degree 1 and 2. Furthermore, we end the classification of separating and non-separating real algebraic curves of bidegree $(5,5)$ in the quadric ellipsoid
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Kleven, Stephanie. "Counting points of bounded height on del Pezzo surfaces." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2948.

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del Pezzo surfaces are isomorphic to either P1 x P1 or P2 blown up a times, where a ranges from 0 to 8. We will look at lines on del Pezzo surfaces isomorphic to P2 blown up a times with a ranging from 0 to 6. We will show that when we count points of bounded height on one of these surfaces, the number of points on lines give us the primary growth order, but the secondary growth order calculates the number of points on the rest of the surface and hence is a better representation of the geometry of the surface.
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Martinez, Garcia Jesus. "Dynamic alpha-invariants of del Pezzo surfaces with boundary." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8090.

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The global log canonical threshold, algebraic counterpart to Tian's alpha-invariant, plays an important role when studying the geometry of Fano varieties. In particular, Tian showed that Fano manifolds with big alpha-invariant can be equipped with a Kahler-Einstein metric. In recent years Donaldson drafted a programme to precisely determine when a smooth Fano variety X admits a Kahler-Einstein metric. It was conjectured that the existence of such a metric is equivalent to X being K-stable, an algebraic-geometric property. A crucial step in Donaldson's programme consists on finding a Kahler-Einstein metric with edge singularities of small angle along a smooth anticanonical boundary. Jeffres, Mazzeo and Rubinstein showed that a dynamic version of the alpha-invariant could be used to find such metrics. The global log canonical threshold measures how anticanonical pairs fail to be log canonical. In this thesis we compute the global log canonical threshold of del Pezzo surfaces in various settings. First we extend Cheltsov's computation of the global log canonical threshold of complex del Pezzo surfaces to non-singular del Pezzo surfaces over a ground field which is algebraically closed and has arbitrary characteristic. Then we study which anticanonical pairs fail to be log canonical. In particular, we give a very explicit classifiation of very singular anticanonical pairs for del Pezzo surfaces of degree smaller or equal than 3. We conjecture under which circumstances such a classifcation is plausible for an arbitrary Fano variety and derive several consequences. As an application, we compute the dynamic alpha-invariant on smooth del Pezzo surfaces of small degree, where the boundary is any smooth elliptic curve C. Our main result is a computation of the dynamic alpha-invariant on all smooth del Pezzo surfaces with boundary any smooth elliptic curve C. The values of the alpha-invariant depend on the choice of C. We apply our computation to find Kahler-Einstein metrics with edge singularities of angle β along C.
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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.

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Les surfaces del Pezzo sont des surfaces algébriques dotées de propriétés particulières, et qui jouent un rôle important dans la classification des surfaces algébriques projectives à transformations birationnelles près.La classification des surfaces del Pezzo rationnelles et lisses de degré d sur un corps parfait arbitraire est classique pour d = 7, 8, 9 et nouvelle pour d = 6. Il en va de même pour ladescription de leurs groupes d'automorphismes. Leur classification et la description de leursgroupes d'automorphismes sont beaucoup plus difficiles pour d ≤ 5, comme on peut déjà le voir si le corps de base est le corps des nombres réels, et la classification est ouverte sur un corps parfait général. Des classifications partielles existent sur des corps finis. Par conséquent, nous ne connaissons pas leurs groupes d'automorphismes en général.L'objectif de la thèse est de classifier les surfaces del Pezzo rationnelles lisses de degréd = 5 et d = 4 sur un corps parfait arbitraire et de décrire leurs groupes d'automorphismes.En raison de la difficulté du projet, le cas d = 4 ne sera étudié que sur le corps des nombres réels
Del 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
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Festi, D. "Topics in the arithmetic of Del Pezzo and K3 surfaces." Doctoral thesis, Università degli Studi di Milano, 2016. http://hdl.handle.net/2434/411137.

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In this thesis we study the arithmetic of certain del Pezzo surfaces and K3 surfaces.We prove that all the del Pezzo surfaces of degree 2 over a finite field are unirational. We compute the Picard lattice of the members of a family of K3 surfaces given by double covers of the projective plane. Finally, we provide an explicit example of a K3 surface over the field of rational numbers with a particular Picard lattice of rank 2.
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Testa, Damiano. "The Severi problem for rational curves on del Pezzo surfaces." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/30356.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 141-142).
Let X be a smooth projective surface and choose a curve C on X. Let VC be the set of all irreducible divisors on X linearly equivalent to C whose normalization is a rational curve. The Severi problem for rational curves on X with divisor class [C] consists of studying the irreducibility of the spaces VC as C varies among all curves on X. In this thesis, we prove that all the spaces VC are irreducible in the case where X is a del Pezzo surface of degree at least two. If the degree of X is one, then we prove the same result only for a general X, with the exception of V-KX, where KX is the canonical divisor of X. It is well known that for general del Pezzo surface of degree one, V-KX consists of twelve points, and thus cannot be irreducible.
by Damiano Testa.
Ph.D.
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Books on the topic "Surfaces del Pezzo"

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V, Nikulin V., ed. Del Pezzo and K3 surfaces. Tokyo: Mathematical Society of Japan, 2006.

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Kunyavskiĭ, B. E. Del Pezzo surfaces of degree four. Paris: Société mathématique de France, 1989.

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Pirozhkov, Dmitrii. Admissible subcategories of del Pezzo surfaces. [New York, N.Y.?]: [publisher not identified], 2020.

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Nakayama, Noboru. Classification of log del Pezzo surfaces of index two. Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University, 2006.

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Maddock, Zachary Alexander. Del Pezzo surfaces with irregularity and intersection numbers on quotients in geometric invariant theory. [New York, N.Y.?]: [publisher not identified], 2012.

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Del Pezzo and K3 Surfaces. Tokyo, Japan: The Mathematical Society of Japan, 2006. http://dx.doi.org/10.2969/msjmemoirs/015010000.

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Robbiani, Marcello. On the arithmetic of toric Del Pezzo surfaces. 1996.

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Book chapters on the topic "Surfaces del Pezzo"

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Várilly-Alvarado, Anthony. "Arithmetic of Del Pezzo surfaces." In Birational Geometry, Rational Curves, and Arithmetic, 293–319. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6482-2_12.

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Cheltsov, Ivan. "Del Pezzo Surfaces and Local Inequalities." In Springer Proceedings in Mathematics & Statistics, 83–101. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05681-4_5.

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Belousov, Grigory. "Cylinders in Del Pezzo Surfaces of Degree Two." In Springer Proceedings in Mathematics & Statistics, 17–70. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-17859-7_2.

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Neitzke, Andrew. "A Mysterious Duality: M-Theory And Del Pezzo Surfaces." In Progress in String, Field and Particle Theory, 441–44. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-010-0211-0_34.

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Tschinkel, Yuri, and Kaiqi Yang. "Potentially Stably Rational Del Pezzo Surfaces over Nonclosed Fields." In Combinatorial and Additive Number Theory III, 227–33. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31106-3_17.

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Swinnerton-Dyer, Peter. "Weak Approximation on Del Pezzo Surfaces of Degree 4." In Progress in Mathematics, 235–57. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8170-8_14.

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Liedtke, Christian. "Morphisms to Brauer–Severi Varieties, with Applications to Del Pezzo Surfaces." In Geometry Over Nonclosed Fields, 157–96. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49763-1_6.

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Petracci, Andrea. "A 1-Dimensional Component of K-Moduli of del Pezzo Surfaces." In Springer Proceedings in Mathematics & Statistics, 709–23. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-17859-7_36.

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Kojima, Hideo. "Singularities of Normal Log Canonical del Pezzo Surfaces of Rank One." In Polynomial Rings and Affine Algebraic Geometry, 199–208. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42136-6_8.

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Wittenberg, Olivier. "Principe de Hasse pour les surfaces de del Pezzo de degré 4." In Intersections de deux quadriques et pinceaux de courbes de genre 1, 109–200. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-69141-9_3.

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Conference papers on the topic "Surfaces del Pezzo"

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BROWNING, TIM D. "RESENT PROGRESS ON THE QUANTITATIVE ARITHMETIC OF DEL PEZZO SURFACES." In Proceedings of the 5th China-Japan Seminar. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814289924_0001.

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Harrison, Michael, and Josef Schicho. "Rational parametrisation for degree 6 Del Pezzo surfaces using lie algebras." In the 2006 international symposium. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1145768.1145794.

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