Quotients of cubic surfaces

被引：4

作者：

Trepalin, Andrey ^{[1
,2
]}

机构：

[1] Inst Informat Transmiss Problems, 19 Bolshoy Karetnyi, Moscow 127994, Russia

[2] Natl Res Univ, Higher Sch Econ, Lab Algebra Geometry, 7 Vavilova Str, Moscow 117312, Russia

来源：

EUROPEAN JOURNAL OF MATHEMATICS | 2016年 / 2卷 / 01期

关键词：

Rationality problems; del Pezzo surfaces; Minimal model program; Cremona group;

D O I：

10.1007/s40879-015-0075-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let k be any field of characteristic zero, X a smooth cubic surface in P-k(3) and G a group acting on X. We show that if X(k) not equal empty set and G is not trivial and not a group of order 3 acting in a special way then the quotient surface X/G is rational over k. For the group G of order 3 we construct examples of both rational and nonrational quotients of both rational and nonrational G-minimal cubic surfaces over k.

引用

页码：333 / 359

页数：27