Describing toric varieties and their equivariant cohomology

• Autorzy: Matthias Franz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57Q15: Triangulating manifolds
• 55N91: Equivariant homology and cohomology
• 14M25: Toric varieties, Newton polyhedra

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 121
• Numer: 1
• Strony: 1-16

Daty

wydano

2010

Twórcy

autor

Matthias Franz

• Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada

Identyfikatory

DOI

10.4064/cm121-1-1