The construction problem for Hodge numbers modulo an integer in positive characteristic

Remy van Dobben de Bruyn, Matthias Paulsen

Published 2020-02-18Version 1

Let $k$ be an algebraically closed field of positive characteristic. For any integer $m \geq 2$, we show that the Hodge numbers of a smooth projective $k$-variety can take on any combination of values modulo $m$, subject only to Serre duality. In particular, there are no non-trivial polynomial relations between the Hodge numbers.