Geodesic
Describing toric varieties and their equivariant cohomology
Matthias Franz1
1 Department of Mathematics University of Western Ontario London, Ontario N6A 5B7, Canada
Colloquium Mathematicum, Tome 121 (2010) no. 1, pp. 1-16 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm121-1-1
Keywords: topologically compact toric varieties constructed identification spaces quotients product compact torus order complex fan detailed proof extend non compact draw several mostly cohomological conclusions particular equivariant integral cohomology toric variety described terms piecewise polynomials fan ordinary integral cohomology concentrated even degrees generalizes result bahri franz ray non compact investigate torsion phenomena integral cohomology

Matthias Franz 1

1 Department of Mathematics University of Western Ontario London, Ontario N6A 5B7, Canada 
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Matthias Franz. Describing toric varieties and their equivariant cohomology. Colloquium Mathematicum, Tome 121 (2010) no. 1, pp. 1-16. doi: 10.4064/cm121-1-1

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