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arXiv · 2002.07733

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

Remy van Dobben de Bruyn·Matthias Paulsen
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Abstract

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.

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Remy van Dobben de Bruyn, Matthias Paulsen. 2020-02-18. The construction problem for Hodge numbers modulo an integer in positive characteristic. https://doi.org/10.1017/fms.2020.48

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