Integral cohomology of singular toric varieties

  • Date: 10/16/2006

Sam Payne (Clay Institute/Stanford University)


University of British Columbia


The singular cohomology and Chow cohomology, with Q-coefficients, of
projective toric varieties with at worst orbifold singularities are
well-understood, but interesting problems remain for toric varieties
with more serious singularities and for cohomology with Z-coefficients.
I will present a computation of the equivariant Chow cohomology of
singular toric varieties with Z-coefficients in terms of
piecewise-polynomial functions on fans, using Kimura's inductive
methods with envelopes and resolutions of singularities. As time
premits, I will also discuss some open questions and conjectures about
the singular cohomology of toric varieties and its relation to Chow
cohomology, and about the cohomology of real toric varieties.

Other Information: 

Algebraic Geometry Seminar 2006