An atlas of K3 surfaces with finite automorphism group

被引：3

作者：

Roulleau, Xavier ^{[1
]}

机构：

[1] Aix Marseille Univ, CNRS, Cent Marseille, I2M,UMR 7373, F-13453 Marseille, France

来源：

EPIJOURNAL DE GEOMETRIE ALGEBRIQUE | 2022年 / 6卷

关键词：

  K3; surfaces; finite automorphism groups; finite number of (-2)-curves; Vinberg algorithms; COX RINGS; PROJECTIVE MODELS; CURVES; FAMILIES; MODULI;

D O I：

10.48550/arXiv.2003.08985

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the geometry of K3 surfaces with finite automorphism group and Picard number at least 3. We describe these surfaces classified by Nikulin and Vinberg as double covers of simpler surfaces or as embedded in a projective space. We study, moreover, the configurations of their finite set of (-2)-curves.

引用

页数：95

共 50 条

[41] K3 SURFACES
BEAUVILLE, A
[J]. ASTERISQUE, 1983, (105-) : 217 - 229
[42] K3 surfaces with a non-symplectic automorphism and product-quotient surfaces with cyclic groups
Garbagnati, Alice
Penegini, Matteo
[J]. REVISTA MATEMATICA IBEROAMERICANA, 2015, 31 (04) : 1277 - 1310
[43] K3 SURFACE ENTROPY AND AUTOMORPHISM GROUPS
Yu, Xun
[J]. JOURNAL OF ALGEBRAIC GEOMETRY, 2024,
[44] Finite-dimensionality and cycles on powers of K3 surfaces
Yin, Qizheng
[J]. COMMENTARII MATHEMATICI HELVETICI, 2015, 90 (02) : 503 - 511
[45] Finite Abelian Groups of K3 Surfaces with Smooth Quotient
Taro Hayashi
[J]. Chinese Annals of Mathematics, Series B, 2023, 44 : 99 - 162
[46] The maximum order of finite groups of automorphisms of K3 surfaces
Kondo, S
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1999, 121 (06) : 1245 - 1252
[47] Finite Abelian Groups of K3 Surfaces with Smooth Quotient
Hayashi, Taro
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2023, 44 (01) : 99 - 162
[48] SYMPLECTIC AUTOMORPHISMS OF K3 SURFACES OF ARBITRARY FINITE ORDER
Huybrechts, Daniel
[J]. MATHEMATICAL RESEARCH LETTERS, 2012, 19 (04) : 947 - 951
[49] The Tate conjecture for K3 surfaces over finite fields
Charles, Francois
[J]. INVENTIONES MATHEMATICAE, 2013, 194 (01) : 119 - 145
[50] Finite Abelian Groups of K3 Surfaces with Smooth Quotient
Taro HAYASHI
[J]. Chinese Annals of Mathematics,Series B, 2023, (01) : 99 - 162

← 1 2 3 4 5 →