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

Abstract

Let k be an algebraically closed field of positive characteristic. For any integer $m\ge 2$ , 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.

Keywords

• 14F99
• 14G17
• 14A10
• 14E99