University of Toronto's Symplectic Geometry Seminar

June 18, 2007, 2:10pm
BA 6183

Matthias Franz

Cohomology of toric varieties and their real parts

Abstract: Any (not necessarily smooth or compact) toric variety comes equipped with an involution, namely complex conjugation. Its fixed point set is the associated real toric variety. In the smooth compact case there is a degree-halving isomorphism between the cohomology algebras (with coefficients in Z/2) of the two spaces. This is false in general, but one may ask whether toric varieties are "maximal" in the sense that the Betti sum of the complex variety equals that of the real part. I will consider this question, and I will present certain "mutants" of toric spaces which turn out to have very peculiar cohomology.