The construction problem for Hodge numbers

The construction problem for Hodge numbers

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Stefan Schreieder, University of Bonn
IAS Room S-101

What are the possible Hodge numbers of a smooth complex projective variety? We construct enough varieties to show that many of the Hodge numbers can take all possible values satisfying the constraints given by Hodge theory. For example, there are varieties such that a Hodge number hp,0 is big and the intermediate Hodge numbers hi,p−i are small.