Describing toric varieties and their equivariant cohomology

Matthias Franz. "Describing toric varieties and their equivariant cohomology." Colloquium Mathematicae 121.1 (2010): 1-16. <http://eudml.org/doc/284224>.

@article{MatthiasFranz2010,
abstract = {Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw several, mostly cohomological conclusions. In particular, we show that the equivariant integral cohomology of a toric variety can be described in terms of piecewise polynomials on the fan if the ordinary integral cohomology is concentrated in even degrees. This generalizes a result of Bahri-Franz-Ray to the non-compact case. We also investigate torsion phenomena in integral cohomology.},
author = {Matthias Franz},
journal = {Colloquium Mathematicae},
language = {eng},
number = {1},
pages = {1-16},
title = {Describing toric varieties and their equivariant cohomology},
url = {http://eudml.org/doc/284224},
volume = {121},
year = {2010},
}

TY - JOUR
AU - Matthias Franz
TI - Describing toric varieties and their equivariant cohomology
JO - Colloquium Mathematicae
PY - 2010
VL - 121
IS - 1
SP - 1
EP - 16
AB - Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw several, mostly cohomological conclusions. In particular, we show that the equivariant integral cohomology of a toric variety can be described in terms of piecewise polynomials on the fan if the ordinary integral cohomology is concentrated in even degrees. This generalizes a result of Bahri-Franz-Ray to the non-compact case. We also investigate torsion phenomena in integral cohomology.
LA - eng
UR - http://eudml.org/doc/284224
ER -