# University of Toronto's Symplectic Geometry Seminar

June 18, 2007, 2:10pm

BA 6183

## Matthias Franz

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## 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.