Cohomologie des variétés moment-angle

Roman Krutowski
University of California (UCLA), Los Angeles
https://www.researchgate.net/profile/Roman-Krutowski-2

Date(s) : 30/04/2021 iCal
11h00 - 12h00

Basic cohomology of moment-angle manifolds

I will start by reminding the construction of toric varieties. These are algebraic varieties associated with rational fans. In the case of a non-rational fan, there is no such pleasant way to define associated manifold with it. However, we still can find some geometric structures. Namely, for a complete fan Σ there is a certain foliation on the so-called moment-angle manifold Z_Σ. I will explain in what sense these foliations generalize toric varieties.
From this perspective, basic cohomology rings of these foliations may be regarded as generalized cohomology rings of toric varieties. During the talk, i am going to present a result on the calculation of basic Dolbeault cohomology of these foliations generalizing the Danilov theorem for toric varieties.