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Готові списки джерел за темами / Birational geometry of surfaces / Статті в журналах

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Статті в журналах з теми "Birational geometry of surfaces"

Автор: Grafiati

Опубліковано: 8 березня 2025

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1

Ciliberto, Ciro, Thomas Dedieu, Flaminio Flamini, and Rita Pardini. "Birational geometry of surfaces." Bollettino dell'Unione Matematica Italiana 11, no. 1 (March 2018): 1–3. http://dx.doi.org/10.1007/s40574-018-0157-1.

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2

Mella, Massimiliano. "Birational geometry of rational quartic surfaces." Journal de Mathématiques Pures et Appliquées 141 (September 2020): 89–98. http://dx.doi.org/10.1016/j.matpur.2020.07.007.

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3

Toda, Yukinobu. "Stability conditions and birational geometry of projective surfaces." Compositio Mathematica 150, no. 10 (July 17, 2014): 1755–88. http://dx.doi.org/10.1112/s0010437x14007337.

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Анотація:

AbstractWe show that the minimal model program on any smooth projective surface is realized as a variation of the moduli spaces of Bridgeland stable objects in the derived category of coherent sheaves.

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4

Chi, Quo-Shin, Luis Fernández, and Hongyou Wu. "Normalized potentials of minimal surfaces in spheres." Nagoya Mathematical Journal 156 (1999): 187–214. http://dx.doi.org/10.1017/s0027763000007133.

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We determine explicitly the normalized potential, a Weierstrass-type representation, of a superconformal surface in an even-dimensional sphere S2n in terms of certain normal curvatures of the surface. When the Hopf differential is zero the potential embodies a system of first order equations governing the directrix curve of a superminimal surface in the twistor space of the sphere. We construct a birational map from the twistor space of S2n into ℂPn(n+1)/2. In general, birational geometry does not preserve the degree of an algebraic curve. However, we prove that the birational map preserves the degree, up to a factor 2, of the twistor lift of a superminimal surface in S6 as long as the surface does not pass through the north pole. Our approach, which is algebro-geometric in nature, accounts in a rather simple way for the aforementioned first order equations, and as a consequence for the particularly interesting class of superminimal almost complex curves in S6. It also yields, in a constructive way, that a generic superminimal surface in S6 is not almost complex and can achieve, by the above degree property, arbitrarily large area.

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5

Blanc, Jérémy, and Frédéric Mangolte. "Geometrically rational real conic bundles and very transitive actions." Compositio Mathematica 147, no. 1 (September 13, 2010): 161–87. http://dx.doi.org/10.1112/s0010437x10004835.

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AbstractIn this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups. We give applications to the classification of real algebraic models of compact surfaces: these applications yield new insight into the geometry of the real locus, proving several surprising facts on this geometry. This geometry can be thought of as a half-way point between the biregular and birational geometries.

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6

Laza, Radu, and Kieran O’Grady. "Birational geometry of the moduli space of quartic surfaces." Compositio Mathematica 155, no. 9 (August 2, 2019): 1655–710. http://dx.doi.org/10.1112/s0010437x19007516.

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Анотація:

By work of Looijenga and others, one understands the relationship between Geometric Invariant Theory (GIT) and Baily–Borel compactifications for the moduli spaces of degree-$2$ $K3$ surfaces, cubic fourfolds, and a few other related examples. The similar-looking cases of degree-$4$ $K3$ surfaces and double Eisenbud–Popescu–Walter (EPW) sextics turn out to be much more complicated for arithmetic reasons. In this paper, we refine work of Looijenga in order to handle these cases. Specifically, in analogy with the so-called Hassett–Keel program for the moduli space of curves, we study the variation of log canonical models for locally symmetric varieties of Type IV associated to $D$-lattices. In particular, for the $19$-dimensional case, we conjecturally obtain a continuous one-parameter interpolation between the GIT and Baily–Borel compactifications for the moduli of degree-$4$ $K3$ surfaces. The analogous $18$-dimensional case, which corresponds to hyperelliptic degree-$4$ $K3$ surfaces, can be verified by means of Variation of Geometric Invariant Theory (VGIT) quotients.

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7

Morrison, David R. "The birational geometry of surfaces with rational double points." Mathematische Annalen 271, no. 3 (September 1985): 415–38. http://dx.doi.org/10.1007/bf01456077.

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8

Ryan, Tim, and Ruijie Yang. "Nef Cones of Nested Hilbert Schemes of Points on Surfaces." International Mathematics Research Notices 2020, no. 11 (May 28, 2018): 3260–94. http://dx.doi.org/10.1093/imrn/rny088.

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Анотація:

Abstract Let X be the projective plane, a Hirzebruch surface, or a general K3 surface. In this paper, we study the birational geometry of various nested Hilbert schemes of points parameterizing pairs of zero-dimensional subschemes on X. We calculate the nef cone for two types of nested Hilbert schemes. As an application, we recover a theorem of Butler on syzygies on Hirzebruch surfaces.

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9

Tanaka, Hiromu. "Minimal Models and Abundance for Positive Characteristic Log Surfaces." Nagoya Mathematical Journal 216 (2014): 1–70. http://dx.doi.org/10.1215/00277630-2801646.

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Анотація:

AbstractWe discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for ℚ-factorial surfaces and for log canonical surfaces. Moreover, in the case where the base field is the algebraic closure of a finite field, we obtain the same results under much weaker assumptions.

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10

Tanaka, Hiromu. "Minimal Models and Abundance for Positive Characteristic Log Surfaces." Nagoya Mathematical Journal 216 (2014): 1–70. http://dx.doi.org/10.1017/s0027763000022431.

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Анотація:

AbstractWe discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for ℚ-factorial surfaces and for log canonical surfaces. Moreover, in the case where the base field is the algebraic closure of a finite field, we obtain the same results under much weaker assumptions.

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11

BIRKAR, CAUCHER, YIFEI CHEN, and LEI ZHANG. "IITAKA CONJECTURE FOR 3-FOLDS OVER FINITE FIELDS." Nagoya Mathematical Journal 229 (November 21, 2016): 21–51. http://dx.doi.org/10.1017/nmj.2016.61.

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Анотація:

We prove Iitaka $C_{n,m}$ conjecture for $3$-folds over the algebraic closure of finite fields. Along the way we prove some results on the birational geometry of log surfaces over nonclosed fields and apply these to existence of relative good minimal models of $3$-folds.

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12

Szabó, Szilárd. "The birational geometry of unramified irregular Higgs bundles on curves." International Journal of Mathematics 28, no. 06 (April 20, 2017): 1750045. http://dx.doi.org/10.1142/s0129167x17500458.

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Анотація:

We give a variant of the Beauville–Narasimhan–Ramanan correspondence for irregular parabolic Higgs bundles on smooth projective curves with fixed semi-simple irregular part and show that it defines a Poisson isomorphism between certain irregular Dolbeault moduli spaces and relative Picard bundles of families of ruled surfaces over the curve.

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13

HASSETT, BRENDAN, and YURI TSCHINKEL. "ABELIAN FIBRATIONS AND RATIONAL POINTS ON SYMMETRIC PRODUCTS." International Journal of Mathematics 11, no. 09 (December 2000): 1163–76. http://dx.doi.org/10.1142/s0129167x00000544.

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Анотація:

Given a variety over a number field, are its rational points potentially dense, i.e. does there exist a finite extension over which rational points are Zariski dense? We study the question of potential density for symmetric products of surfaces. Contrary to the situation for curves, rational points are not necessarily potentially dense on a sufficiently high symmetric product. Our main result is that rational points are potentially dense for the Nth symmetric product of a K3 surface, where N is explicitly determined by the geometry of the surface. The basic construction is that for some N, the Nth symmetric power of a K3 surface is birational to an Abelian fibration over ℙN. It is an interesting geometric problem to find the smallest N with this property.

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14

Wolter, Jonas. "Equivariant birational geometry of quintic del Pezzo surface." European Journal of Mathematics 4, no. 3 (August 13, 2018): 1278–92. http://dx.doi.org/10.1007/s40879-018-0272-7.

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15

Auel, Asher, and Marcello Bernardara. "Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields." Proceedings of the London Mathematical Society 117, no. 1 (February 23, 2018): 1–64. http://dx.doi.org/10.1112/plms.12119.

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16

Fisher, Tom. "Explicit moduli spaces for congruences of elliptic curves." Mathematische Zeitschrift 295, no. 3-4 (September 14, 2019): 1337–54. http://dx.doi.org/10.1007/s00209-019-02392-9.

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Анотація:

Abstract We determine explicit birational models over $${{\mathbb {Q}}}$$ Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell–Weil lattice and the geometric Picard number.

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17

Nuer, Howard. "Projectivity and birational geometry of Bridgeland moduli spaces on an Enriques surface." Proceedings of the London Mathematical Society 113, no. 3 (July 27, 2016): 345–86. http://dx.doi.org/10.1112/plms/pdw033.

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18

Chung, Kiryong, and Han-Bom Moon. "Birational geometry of the moduli space of pure sheaves on quadric surface." Comptes Rendus Mathematique 355, no. 10 (October 2017): 1082–88. http://dx.doi.org/10.1016/j.crma.2017.09.005.

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19

Zhang, Lei. "Surfaces with $$p_g = q= 1$$ p g = q = 1 , $$K^2 = 7$$ K 2 = 7 and non-birational bicanonical maps." Geometriae Dedicata 177, no. 1 (June 18, 2014): 293–306. http://dx.doi.org/10.1007/s10711-014-9990-2.

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20

Zhao, Junyan. "Moduli of genus six curves and K-stability." Transactions of the American Mathematical Society, Series B 11, no. 26 (May 2, 2024): 863–900. http://dx.doi.org/10.1090/btran/195.

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Анотація:

The K-moduli theory provides different compactifications of various moduli spaces, including moduli of curves. As a general genus six curve can be canonically embedded into the smooth quintic del Pezzo surface, we study in this paper the K-moduli spaces M ¯ K ( c ) \overline {M}^K(c) of the quintic log Fano pairs. We classify the strata of genus six curves C C appearing in the K-moduli by explicitly describing the wall-crossing structure. The K-moduli spaces interpolate between two birational moduli spaces constructed by Geometric Invariant Theory (GIT) and moduli of K3 surfaces via Hodge theory.

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21

Tikhomirov, A. S., and T. L. Troshina. "Birational and numerical geometry of the variety of complete pairs of two-point spaces on an algebraic surface." Mathematical Notes 65, no. 3 (March 1999): 344–50. http://dx.doi.org/10.1007/bf02675077.

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22

Totaro, Burt. "Birational geometry of quadrics." Bulletin de la Société mathématique de France 137, no. 2 (2009): 253–76. http://dx.doi.org/10.24033/bsmf.2575.

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23

Birkar, Caucher. "Generalised pairs in birational geometry." EMS Surveys in Mathematical Sciences 8, no. 1 (August 31, 2021): 5–24. http://dx.doi.org/10.4171/emss/42.

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24

IITAKA, Shigeru. "Birational Geometry of Plane Curves." Tokyo Journal of Mathematics 22, no. 2 (December 1999): 289–321. http://dx.doi.org/10.3836/tjm/1270041440.

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25

Kawamata, Yujiro. "Birational geometry and derived categories." Surveys in Differential Geometry 22, no. 1 (2017): 291–317. http://dx.doi.org/10.4310/sdg.2017.v22.n1.a11.

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26

Grassi, Antonella. "Birational geometry old and new." Bulletin of the American Mathematical Society 46, no. 1 (October 27, 2008): 99–123. http://dx.doi.org/10.1090/s0273-0979-08-01233-0.

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27

Gross, Mark, Paul Hacking, and Sean Keel. "Birational geometry of cluster algebras." Algebraic Geometry 2, no. 2 (May 1, 2015): 137–75. http://dx.doi.org/10.14231/ag-2015-007.

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28

Bini, Gilberto, and Claudio Fontanari. "On the birational geometry of." manuscripta mathematica 115, no. 3 (October 1, 2004): 379–87. http://dx.doi.org/10.1007/s00229-004-0497-2.

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29

Bondal, Alexey, Mikhail Kapranov, and Vadim Schechtman. "Perverse schobers and birational geometry." Selecta Mathematica 24, no. 1 (February 9, 2018): 85–143. http://dx.doi.org/10.1007/s00029-018-0395-1.

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30

Wang, Chin-Lung. "Cohomology Theory in Birational Geometry." Journal of Differential Geometry 60, no. 2 (February 2002): 345–54. http://dx.doi.org/10.4310/jdg/1090351105.

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31

Vermeire, Peter. "Secant varieties and birational geometry." Mathematische Zeitschrift 242, no. 1 (February 1, 2002): 75–95. http://dx.doi.org/10.1007/s002090100308.

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32

Rackwitz, H. G. "Birational geometry of complete intersections." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 66, no. 1 (December 1996): 263–71. http://dx.doi.org/10.1007/bf02940808.

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33

Larsen, M., and V. Lunts. "Motivic Measures and Stable Birational Geometry." Moscow Mathematical Journal 3, no. 1 (2003): 85–95. http://dx.doi.org/10.17323/1609-4514-2003-3-1-85-95.

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34

Pukhlikov, A. V. "Birational geometry of singular Fano varieties." Proceedings of the Steklov Institute of Mathematics 264, no. 1 (April 2009): 159–77. http://dx.doi.org/10.1134/s0081543809010180.

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35

Pukhlikov, A. V. "Birational geometry of Fano direct products." Izvestiya: Mathematics 69, no. 6 (December 31, 2005): 1225–55. http://dx.doi.org/10.1070/im2005v069n06abeh002300.

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36

Pukhlikov, A. V. "Birational geometry of Fano double covers." Sbornik: Mathematics 199, no. 8 (August 31, 2008): 1225–50. http://dx.doi.org/10.1070/sm2008v199n08abeh003960.

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37

Bellamy, Gwyn, and Alastair Craw. "Birational geometry of symplectic quotient singularities." Inventiones mathematicae 222, no. 2 (April 30, 2020): 399–468. http://dx.doi.org/10.1007/s00222-020-00972-9.

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Анотація:

Abstract For a finite subgroup $$\Gamma \subset \mathrm {SL}(2,\mathbb {C})$$ Γ ⊂ SL ( 2 , C ) and for $$n\ge 1$$ n ≥ 1 , we use variation of GIT quotient for Nakajima quiver varieties to study the birational geometry of the Hilbert scheme of n points on the minimal resolution S of the Kleinian singularity $$\mathbb {C}^2/\Gamma $$ C 2 / Γ . It is well known that $$X:={{\,\mathrm{{\mathrm {Hilb}}}\,}}^{[n]}(S)$$ X : = Hilb [ n ] ( S ) is a projective, crepant resolution of the symplectic singularity $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n , where $$\Gamma _n=\Gamma \wr \mathfrak {S}_n$$ Γ n = Γ ≀ S n is the wreath product. We prove that every projective, crepant resolution of $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n can be realised as the fine moduli space of $$\theta $$ θ -stable $$\Pi $$ Π -modules for a fixed dimension vector, where $$\Pi $$ Π is the framed preprojective algebra of $$\Gamma $$ Γ and $$\theta $$ θ is a choice of generic stability condition. Our approach uses the linearisation map from GIT to relate wall crossing in the space of $$\theta $$ θ -stability conditions to birational transformations of X over $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n . As a corollary, we describe completely the ample and movable cones of X over $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n , and show that the Mori chamber decomposition of the movable cone is determined by an extended Catalan hyperplane arrangement of the ADE root system associated to $$\Gamma $$ Γ by the McKay correspondence. In the appendix, we show that morphisms of quiver varieties induced by variation of GIT quotient are semismall, generalising a result of Nakajima in the case where the quiver variety is smooth.

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38

Namikawa, Yoshinori. "Induced nilpotent orbits and birational geometry." Advances in Mathematics 222, no. 2 (October 2009): 547–64. http://dx.doi.org/10.1016/j.aim.2009.05.001.

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39

Shibata, Kohsuke. "Multiplicity and invariants in birational geometry." Journal of Algebra 476 (April 2017): 161–85. http://dx.doi.org/10.1016/j.jalgebra.2016.11.027.

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40

Birkar, Caucher. "Some open problems in birational geometry." Notices of the International Consortium of Chinese Mathematicians 11, no. 1 (2023): 83–97. http://dx.doi.org/10.4310/iccm.2023.v11.n1.a9.

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41

Tschinkel, Yuri, Kaiqi Yang, and Zhijia Zhang. "Equivariant birational geometry of linear actions." EMS Surveys in Mathematical Sciences 11, no. 2 (September 24, 2024): 235–76. http://dx.doi.org/10.4171/emss/82.

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42

Hacon, Christopher, Daniel Huybrechts, Richard P. W. Thomas, and Chenyang Xu. "Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects." Oberwolfach Reports 17, no. 2 (July 1, 2021): 977–1021. http://dx.doi.org/10.4171/owr/2020/19.

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43

Hacon, Christopher, Daniel Huybrechts, Richard P. W. Thomas, and Chenyang Xu. "Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects." Oberwolfach Reports 19, no. 3 (June 13, 2023): 1805–64. http://dx.doi.org/10.4171/owr/2022/32.

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44

Occhetta, Gianluca, Eleonora Romano, Luis Solá Conde та Jarosław Wiśniewski. "Small bandwidth ℂ*-actions and birational geometry". Journal of Algebraic Geometry 32, № 1 (8 червня 2022): 1–57. http://dx.doi.org/10.1090/jag/808.

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Анотація:

In this paper we study smooth projective varieties and polarized pairs with an action of a one dimensional complex torus. As a main tool, we define birational geometric counterparts of these actions, that, under certain assumptions, encode the information necessary to reconstruct them. In particular, we consider some cases of actions of low complexity—measured in terms of two invariants of the action, called bandwidth and bordism rank—and discuss how they are determined by well known birational transformations, namely Atiyah flips and Cremona transformations.

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45

Hassett, Brendan, and Yuri Tschinkel. "Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces." Journal of the Institute of Mathematics of Jussieu 9, no. 1 (August 11, 2009): 125–53. http://dx.doi.org/10.1017/s1474748009000140.

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Анотація:

AbstractWe study the birational geometry of irreducible holomorphic symplectic varieties arising as varieties of lines of general cubic fourfolds containing a cubic scroll. We compute the ample and moving cones, and exhibit a birational automorphism of infinite order explaining the chamber decomposition of the moving cone.

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46

Schmidt, Benjamin. "On the birational geometry of Schubert varieties." Bulletin de la Société mathématique de France 143, no. 3 (2015): 489–502. http://dx.doi.org/10.24033/bsmf.2696.

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47

Kawamata, Yujiro. "Book Review: Birational geometry of algebraic varieties." Bulletin of the American Mathematical Society 38, no. 02 (February 7, 2001): 267–73. http://dx.doi.org/10.1090/s0273-0979-01-00910-7.

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48

Pukhlikov, A. V. "Birational geometry of higher-dimensional Fano varieties." Proceedings of the Steklov Institute of Mathematics 288, S2 (April 2015): 1–150. http://dx.doi.org/10.1134/s0081543815030013.

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49

Totaro, Burt. "Birational geometry of quadrics in characteristic $2$." Journal of Algebraic Geometry 17, no. 3 (September 1, 2008): 577–97. http://dx.doi.org/10.1090/s1056-3911-08-00472-4.

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50

Mongardi, Giovanni, and Antonio Rapagnetta. "Monodromy and birational geometry of O'Grady's sixfolds." Journal de Mathématiques Pures et Appliquées 146 (February 2021): 31–68. http://dx.doi.org/10.1016/j.matpur.2020.12.006.

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