Thin monodromy in Sp(4)

被引：27

作者：

Brav, Christopher ^{[1
]}

Thomas, Hugh ^{[2
]}

机构：

[1] Univ Oxford, Math Inst, Oxford OX1 3LB, England

[2] Univ New Brunswick, Dept Math & Stat, Fredericton, NB E3B 5A3, Canada

来源：

COMPOSITIO MATHEMATICA | 2014年 / 150卷 / 03期

基金：

英国工程与自然科学研究理事会; 加拿大自然科学与工程研究理事会;

关键词：

Dwork family; monodromy; thin groups; ping-pong lemma;

D O I：

10.1112/S0010437X13007550

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that some hypergeometric monodromy groups in Sp(4, Z) split as free or amalgamated products and hence by cohomological considerations give examples of Zariski dense, non-arithmetic monodromy groups of real rank 2. In particular, we show that the monodromy group of the natural quotient of the Dwork family of quintic threefolds in P-4 splits as Z * Z/5Z. As a consequence, for a smooth quintic threefold X we show that the group of autoequivalences D-b(X) generated by the spherical twist along Ox and by tensoring with O-X(1) is an Artin group of dihedral type.

引用

页码：333 / 343

页数：11

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