# Constructing varieties with prescribed Hodge numbers modulo m in positive characteristic

Friday, April 30, 2021 12:00 PM

Remy van Dobben de Bruyn (Princeton/IAS)

The inverse Hodge problem asks which possible Hodge diamonds can occur for smooth projective varieties. While this is a very hard problem in general, Paulsen and Schreieder recently showed that in characteristic 0 there are no restrictions on the modulo m Hodge numbers, besides the usual symmetries. In joint work with Matthias Paulsen, we extend this to positive characteristic, where the story is more intricate.