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Journal articles on the topic 'Surfaces del Pezzo'

Author: Grafiati

Published: 8 March 2025

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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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Kuznetsov, Alexander Gennad'evich, and Yuri Gennadievich Prokhorov. "On higher-dimensional del Pezzo varieties." Известия Российской академии наук. Серия математическая 87, no. 3 (2023): 75–148. http://dx.doi.org/10.4213/im9385.

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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. Bibliography: 41 titles.

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12

Hacking, Paul, and Yuri Prokhorov. "Smoothable del Pezzo surfaces with quotient singularities." Compositio Mathematica 146, no. 1 (December 15, 2009): 169–92. http://dx.doi.org/10.1112/s0010437x09004370.

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AbstractWe classify del Pezzo surfaces with quotient singularities and Picard rank one which admit a ℚ-Gorenstein smoothing. These surfaces arise as singular fibres of del Pezzo fibrations in the 3-fold minimal model program and also in moduli problems.

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13

Bocklandt, Raf. "Toric systems and mirror symmetry." Compositio Mathematica 149, no. 11 (August 28, 2013): 1839–55. http://dx.doi.org/10.1112/s0010437x1300701x.

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AbstractIn their paper [Exceptional sequences of invertible sheaves on rational surfaces, Compositio Math. 147 (2011), 1230–1280], Hille and Perling associate to every cyclic full strongly exceptional sequence of line bundles on a toric weak del Pezzo surface a toric system, which defines a new toric surface. We interpret this construction as an instance of mirror symmetry and extend it to a duality on the set of toric weak del Pezzo surfaces equipped with a cyclic full strongly exceptional sequence.

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14

Beheshti, Roya, Brian Lehmann, Eric Riedl, and Sho Tanimoto. "Rational curves on del Pezzo surfaces in positive characteristic." Transactions of the American Mathematical Society, Series B 10, no. 14 (March 6, 2023): 407–51. http://dx.doi.org/10.1090/btran/138.

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We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most primes p p we prove the irreducibility of the moduli space of rational curves of a given nef class, extending results of Testa in characteristic 0 0 . We also investigate the principles of Geometric Manin’s Conjecture for weak del Pezzo surfaces. In the course of this investigation, we give examples of weak del Pezzo surfaces defined over F 2 ( t ) \mathbb F_2(t) or F 3 ( t ) \mathbb {F}_{3}(t) such that the exceptional sets in Manin’s Conjecture are Zariski dense.

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15

Oneto, Alessandro, and Andrea Petracci. "On the quantum periods of del Pezzo surfaces with ⅓ (1, 1) singularities." Advances in Geometry 18, no. 3 (July 26, 2018): 303–36. http://dx.doi.org/10.1515/advgeom-2017-0048.

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AbstractIn earlier joint work with collaborators we gave a conjectural classification of a broad class of orbifold del Pezzo surfaces, using Mirror Symmetry. We proposed that del Pezzo surfaces X with isolated cyclic quotient singularities such that X admits a ℚ-Gorenstein toric degeneration correspond via Mirror Symmetry to maximally mutable Laurent polynomials f in two variables, and that the quantum period of such a surface X, which is a generating function for Gromov–Witten invariants of X, coincides with the classical period of its mirror partner f.In this paper we give strong evidence for this conjecture. Contingent on conjectural generalisations of the Quantum Lefschetz theorem and the Abelian/non-Abelian correspondence, we compute many quantum periods for del Pezzo surfaces with $\begin{array}{} \frac{1}{3} \end{array} $(1, 1) singularities. Our computations also give strong evidence for the extension of these two principles to the orbifold setting.

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16

Cheltsov, Ivan, Jihun Park, and Joonyeong Won. "Cylinders in singular del Pezzo surfaces." Compositio Mathematica 152, no. 6 (April 21, 2016): 1198–224. http://dx.doi.org/10.1112/s0010437x16007284.

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For each del Pezzo surface $S$ with du Val singularities, we determine whether it admits a $(-K_{S})$-polar cylinder or not. If it allows one, then we present an effective $\mathbb{Q}$-divisor $D$ that is $\mathbb{Q}$-linearly equivalent to $-K_{S}$ and such that the open set $S\setminus \text{Supp}(D)$ is a cylinder. As a corollary, we classify all the del Pezzo surfaces with du Val singularities that admit non-trivial $\mathbb{G}_{a}$-actions on their affine cones defined by their anticanonical divisors.

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17

Ren, Qingchun, Kristin Shaw, and Bernd Sturmfels. "Tropicalization of del Pezzo surfaces." Advances in Mathematics 300 (September 2016): 156–89. http://dx.doi.org/10.1016/j.aim.2016.03.017.

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18

Grinenko, M. M. "Fibrations into del Pezzo surfaces." Russian Mathematical Surveys 61, no. 2 (April 30, 2006): 255–300. http://dx.doi.org/10.1070/rm2006v061n02abeh004312.

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19

Landesman, Aaron, and Anand Patel. "Interpolation problems: Del Pezzo surfaces." ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE 19, no. 4 (2019): 1389–428. http://dx.doi.org/10.2422/2036-2145.201702_019.

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20

Cheltsov, Ivan, and Jesus Martinez-Garcia. "Unstable polarized del Pezzo surfaces." Transactions of the American Mathematical Society 372, no. 10 (August 5, 2019): 7255–96. http://dx.doi.org/10.1090/tran/7900.

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21

Cheltsov, Ivan, and Jesus Martinez-Garcia. "Stable Polarized del Pezzo Surfaces." International Mathematics Research Notices 2020, no. 18 (July 26, 2018): 5477–505. http://dx.doi.org/10.1093/imrn/rny182.

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Abstract We give a simple sufficient condition for $K$-stability of polarized del Pezzo surfaces and for the existence of a constant scalar curvature Kähler metric in the Kähler class corresponding to the polarization.

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22

Derenthal, Ulrich, and Daniel Loughran. "Equivariant Compactifications of Two-Dimensional Algebraic Groups." Proceedings of the Edinburgh Mathematical Society 58, no. 1 (October 27, 2014): 149–68. http://dx.doi.org/10.1017/s001309151400042x.

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AbstractWe classify generically transitive actions of semi-direct products on ℙ2. Motivated by the program to study the distribution of rational points on del Pezzo surfaces (Manin's conjecture), we determine all (possibly singular) del Pezzo surfaces that are equivariant compactifications of homogeneous spaces for semi-direct products .

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23

BANWAIT, BARINDER, FRANCESC FITÉ, and DANIEL LOUGHRAN. "Del Pezzo surfaces over finite fields and their Frobenius traces." Mathematical Proceedings of the Cambridge Philosophical Society 167, no. 01 (April 10, 2018): 35–60. http://dx.doi.org/10.1017/s0305004118000166.

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AbstractLet S be a smooth cubic surface over a finite field $\mathbb{F}$q. It is known that #S($\mathbb{F}$q) = 1 + aq + q2 for some a ∈ {−2, −1, 0, 1, 2, 3, 4, 5, 7}. Serre has asked which values of a can arise for a given q. Building on special cases treated by Swinnerton–Dyer, we give a complete answer to this question. We also answer the analogous question for other del Pezzo surfaces, and consider the inverse Galois problem for del Pezzo surfaces over finite fields. Finally we give a corrected version of Manin's and Swinnerton–Dyer's tables on cubic surfaces over finite fields.

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24

Zhang, D. Q. "Algebraic surfaces with nef and big anti-canonical divisor." Mathematical Proceedings of the Cambridge Philosophical Society 117, no. 1 (January 1995): 161–63. http://dx.doi.org/10.1017/s0305004100072984.

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Let S be a normal projective algebraic surface over C with at worst quotient singularities. S is a quasi-log del Pezzo surface if the anti-canonical divisor — Ks is nef (= numerically effective) and big, i.e. — Ks. C ≥ 0 for all curves C on S and (−Ks)2 > 0. Further, if — Ks is ample we say S is a log del Pezzo surface.

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25

Zaitsev, Alexandr Vladimirovich. "Forms of del Pezzo surfaces of degree $5$ and $6$." Sbornik: Mathematics 214, no. 6 (2023): 816–31. http://dx.doi.org/10.4213/sm9686e.

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We obtain necessary and sufficient condition for the existence of del Pezzo surfaces of degrees $5$ and $6$ over a field $K$ with a prescribed action of absolute Galois group $\operatorname{Gal}(K^{\mathrm{sep}}/K)$ on the graph of $(-1)$-curves. We also compute the automorphism groups of del Pezzo surfaces of degree $5$ over arbitrary fields. Bibliography: 19 titles.

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26

Coskun, Emre, and Ozhan Genc. "Ulrich trichotomy on del Pezzo surfaces." Advances in Geometry 23, no. 1 (January 1, 2023): 51–68. http://dx.doi.org/10.1515/advgeom-2022-0024.

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Abstract We use a correspondence between Ulrich bundles on a projective variety and quiver representations to prove that certain del Pezzo surfaces satisfy the Ulrich trichotomy, for any given polarization.

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27

Lin, Chin-Yi. "A Non-vanishing Theorem of Del Pezzo Surfaces." Proceedings of the Edinburgh Mathematical Society 59, no. 2 (March 3, 2016): 463–72. http://dx.doi.org/10.1017/s001309151500022x.

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28

Corti, Alessio. "Del Pezzo Surfaces Over Dedekind Schemes." Annals of Mathematics 144, no. 3 (November 1996): 641. http://dx.doi.org/10.2307/2118567.

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29

Serganova, Vera, and Alexei Skorobogatov. "Del Pezzo surfaces and representation theory." Algebra & Number Theory 1, no. 4 (November 1, 2007): 393–419. http://dx.doi.org/10.2140/ant.2007.1.393.

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30

LANTERI, Antonio, Marino PALLESCHI, and Andrew J. SOMMESE. "Del Pezzo surfaces as hyperplane sections." Journal of the Mathematical Society of Japan 49, no. 3 (July 1997): 501–29. http://dx.doi.org/10.2969/jmsj/04930501.

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31

SchrÖer, Stefan. "Weak del Pezzo surfaces with irregularity." Tohoku Mathematical Journal 59, no. 2 (2007): 293–322. http://dx.doi.org/10.2748/tmj/1182180737.

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32

Kunyavskij, B. Eh, A. N. Skorobogatov, and M. A. Tsfasman. "Del Pezzo surfaces of degree four." Mémoires de la Société mathématique de France 1 (1989): 1–113. http://dx.doi.org/10.24033/msmf.338.

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33

Evans, J. D. "Lagrangian spheres in Del Pezzo surfaces." Journal of Topology 3, no. 1 (2010): 181–227. http://dx.doi.org/10.1112/jtopol/jtq004.

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34

Maddock, Zachary. "Regular del Pezzo surfaces with irregularity." Journal of Algebraic Geometry 25, no. 3 (February 24, 2016): 401–29. http://dx.doi.org/10.1090/jag/650.

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35

Coray, D. F., and M. A. Tsfasman. "Arithmetic on Singular Del Pezzo Surfaces." Proceedings of the London Mathematical Society s3-57, no. 1 (July 1988): 25–87. http://dx.doi.org/10.1112/plms/s3-57.1.25.

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36

Kuleshov, S. A., and D. O. Orlov. "EXCEPTIONAL SHEAVES ON DEL PEZZO SURFACES." Russian Academy of Sciences. Izvestiya Mathematics 44, no. 3 (June 30, 1995): 479–513. http://dx.doi.org/10.1070/im1995v044n03abeh001609.

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37

Chan, Daniel, and Rajesh S. Kulkarni. "Del Pezzo orders on projective surfaces." Advances in Mathematics 173, no. 1 (January 2003): 144–77. http://dx.doi.org/10.1016/s0001-8708(02)00020-8.

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38

Trepalin, Andrey. "Del Pezzo surfaces over finite fields." Finite Fields and Their Applications 68 (December 2020): 101741. http://dx.doi.org/10.1016/j.ffa.2020.101741.

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39

Hitchin, Nigel. "Bihermitian metrics on Del Pezzo surfaces." Journal of Symplectic Geometry 5, no. 1 (2007): 1–8. http://dx.doi.org/10.4310/jsg.2007.v5.n1.a2.

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40

YE, Qiang. "On Gorenstein log del Pezzo surfaces." Japanese journal of mathematics. New series 28, no. 1 (2002): 87–136. http://dx.doi.org/10.4099/math1924.28.87.

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41

Corn, Patrick. "Del Pezzo surfaces of degree 6." Mathematical Research Letters 12, no. 1 (2005): 75–84. http://dx.doi.org/10.4310/mrl.2005.v12.n1.a8.

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42

Hong, Wei, and Ping Xu. "Poisson cohomology of Del Pezzo surfaces." Journal of Algebra 336, no. 1 (June 2011): 378–90. http://dx.doi.org/10.1016/j.jalgebra.2010.12.017.

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43

Chel’tsov, I. A. "Del Pezzo surfaces with nonrational singularities." Mathematical Notes 62, no. 3 (September 1997): 377–89. http://dx.doi.org/10.1007/bf02360880.

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44

Cheltsov, Ivan, and Andrew Wilson. "Del Pezzo Surfaces with Many Symmetries." Journal of Geometric Analysis 23, no. 3 (December 8, 2011): 1257–89. http://dx.doi.org/10.1007/s12220-011-9286-9.

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45

Abe, Makoto, and Mikio Furushima. "On non-normal del Pezzo surfaces." Mathematische Nachrichten 260, no. 1 (November 2003): 3–13. http://dx.doi.org/10.1002/mana.200310099.

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46

Miyanishi, M., and D. Q. Zhang. "Gorenstein Log del Pezzo Surfaces, II." Journal of Algebra 156, no. 1 (April 1993): 183–93. http://dx.doi.org/10.1006/jabr.1993.1069.

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47

Pirozhkov, Dmitrii. "Admissible subcategories of del Pezzo surfaces." Advances in Mathematics 424 (July 2023): 109046. http://dx.doi.org/10.1016/j.aim.2023.109046.

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48

Virin, Nikita Andreevich. "Automorphisms of Du Val del Pezzo surfaces." Sbornik: Mathematics 215, no. 12 (2024): 1582–606. https://doi.org/10.4213/sm10052e.

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49

Paemurru, Erik. "Del Pezzo Surfaces in Weighted Projective Spaces." Proceedings of the Edinburgh Mathematical Society 61, no. 2 (April 4, 2018): 545–72. http://dx.doi.org/10.1017/s0013091517000335.

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50

Belousov, Grigory. "Log del Pezzo Surfaces with Simple Automorphism Groups." Proceedings of the Edinburgh Mathematical Society 58, no. 1 (December 10, 2014): 33–52. http://dx.doi.org/10.1017/s0013091514000054.

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