# Rational points and Coxeter group actions on the cohomology of toric varieties

Gustav I. Lehrer^{[1]}

- [1] University of Sydney School of Mathematics and Statistics N.S.W. 2006 (Australia)

Annales de l’institut Fourier (2008)

- Volume: 58, Issue: 2, page 671-688
- ISSN: 0373-0956

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topLehrer, Gustav I.. "Rational points and Coxeter group actions on the cohomology of toric varieties." Annales de l’institut Fourier 58.2 (2008): 671-688. <http://eudml.org/doc/10328>.

@article{Lehrer2008,

abstract = {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.},

affiliation = {University of Sydney School of Mathematics and Statistics N.S.W. 2006 (Australia)},

author = {Lehrer, Gustav I.},

journal = {Annales de l’institut Fourier},

keywords = {Toric varieties; cohomology; Hodge theory; rational points; toric varieties},

language = {eng},

number = {2},

pages = {671-688},

publisher = {Association des Annales de l’institut Fourier},

title = {Rational points and Coxeter group actions on the cohomology of toric varieties},

url = {http://eudml.org/doc/10328},

volume = {58},

year = {2008},

}

TY - JOUR

AU - Lehrer, Gustav I.

TI - Rational points and Coxeter group actions on the cohomology of toric varieties

JO - Annales de l’institut Fourier

PY - 2008

PB - Association des Annales de l’institut Fourier

VL - 58

IS - 2

SP - 671

EP - 688

AB - 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.

LA - eng

KW - Toric varieties; cohomology; Hodge theory; rational points; toric varieties

UR - http://eudml.org/doc/10328

ER -

## References

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