Orders of automorphisms of K3 surfaces

被引：17
作者：
Keum, JongHae [1 ]
机构：
[1] Korea Inst Adv Study, Sch Math, Seoul 130722, South Korea
来源：
ADVANCES IN MATHEMATICS | 2016年 / 303卷
基金：
新加坡国家研究基金会;
关键词：
K3; surfaces; Automorphisms; FINITE-GROUPS; KUMMER SURFACES; NUMBER;
D O I：
10.1016/j.aim.2016.08.014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We determine all orders of automorphisms of complex K3 surfaces and of K3 surfaces in characteristic p > 3. In particular, 66 is the maximum finite order in each characteristic p not equal 2,3. As a consequence, we give a bound for the orders of finite groups acting on K3 surfaces in characteristic p > 7. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：39 / 87
页数：49
相关论文
共 36 条
[1]  
Artin M., 1977, Coverings of the rational double points in characteristic p, P11
[2]  
COSSEC F, 1989, ENRIQUES SURFACES, V1
[3]   INTERSECTION NUMBERS OF SECTIONS OF ELLIPTIC SURFACES [J].
COX, DA ;
ZUCKER, S .
INVENTIONES MATHEMATICAE, 1979, 53 (01) :1-44
[4]   REPRESENTATIONS OF REDUCTIVE GROUPS OVER FINITE-FIELDS [J].
DELIGNE, P ;
LUSZTIG, G .
ANNALS OF MATHEMATICS, 1976, 103 (01) :103-161
[5]  
DELIGNE P, 1981, ALGEBRAIC SURFACES O, V868, P58
[6]  
Dolgachev I, 2001, J ALGEBRAIC GEOM, V10, P101
[7]  
Dolgachev IV, 2009, J EUR MATH SOC, V11, P799
[8]   Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic [J].
Dolgachev, Igor V. ;
Keum, JongHae .
ANNALS OF MATHEMATICS, 2009, 169 (01) :269-313
[9]  
Hwang D, 2011, J ALGEBRAIC GEOM, V20, P495
[10]  
ILLUSIE L., 1975, Proc. Sympos. Pure Math., V29, P459
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