Rational points and coxeter group actions on the cohomology of toric varieties

被引：8

作者：

Lehrer, Gustav I. ^{[1
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

来源：

ANNALES DE L INSTITUT FOURIER | 2008年 / 58卷 / 02期

关键词：

Cohomology; Hodge theory; Rational points; Toric varieties;

D O I：

10.5802/aif.2364

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive a simple formula for the action of a finite crystallographic Coxeter group on the cohomology of its associated complex toric variety, using the method of counting rational points over finite fields, and the Hodge structure of the cohomology. Various applications are given, including the determination of the graded multiplicity of the reflection representation.

引用

页码：671 / 688

页数：18

共 15 条

[1]

[Anonymous], 1990, MOTS

[2]

Bourbaki N, 1968, ACTUALITES SCI IND, V1337

[3]

Carter R. W., 1985, FINITE GROUPS LIE TY

[4]

Danilov V.I., 1978, Uspekhi Mat. Nauk, V33, P85, DOI 10.1070/RM1978v033n02ABEH002305

[5] COHOMOLOGY OF COMPACTIFICATIONS OF ALGEBRAIC-GROUPS [J].

DECONCINI, C ;

PROCESI, C .

DUKE MATHEMATICAL JOURNAL, 1986, 53 (03) :585-594

[6] ON THE GEOMETRY OF QUADRICS AND THEIR DEGENERATIONS [J].

DECONCINI, C ;

GORESKY, M ;

MACPHERSON, R ;

PROCESI, C .

COMMENTARII MATHEMATICI HELVETICI, 1988, 63 (03) :337-413

[7]

DIMCA A, 1997, AUSTR MATH SOC LECT, V9, P161

[8] A CHARACTER FORMULA FOR THE REPRESENTATION OF A WEYL GROUP IN THE COHOMOLOGY OF THE ASSOCIATED TORIC VARIETY [J].

DOLGACHEV, I ;

LUNTS, V .

JOURNAL OF ALGEBRA, 1994, 168 (03) :741-772

[9]

Fulton W., 1993, Annals of Mathematics Studies, V131, DOI DOI 10.1515/9781400882526

[10] Equivariant Poincare polynomials and counting points over finite fields [J].

Kisin, M ;

Lehrer, GI .

JOURNAL OF ALGEBRA, 2002, 247 (02) :435-451

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