Zhi Jiang, Université de Paris-Sud, Orsay, France

Rational cohomology tori

Abstract

We study normal compact Kähler spaces whose rational cohomology rings are isomorphic to that of a complex torus. We call them rational cohomology tori. First, we classify those with rational singularities up to dimension three. Then, we give constraints on the degree of the Albanese morphism and the number of simple factors of the Albanese variety for rational cohomology tori of general type (hence projective) with rational singularities. This is a joint work with Olivier Debarre and Marti Lahoz.