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arXiv · 1903.05430

The construction problem for Hodge numbers modulo an integer

Matthias Paulsen·Stefan Schreieder
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Abstract

For any positive integer m and any dimension n, we show that any n-dimensional Hodge diamond with values in Z/mZ is attained by the Hodge numbers of an n-dimensional smooth complex projective variety. As a corollary, there are no polynomial relations among the Hodge numbers of n-dimensional smooth complex projective varieties besides the ones induced by the Hodge symmetries, which answers a question raised by Kollár in 2012.

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Matthias Paulsen, Stefan Schreieder. 2019-08-02. The construction problem for Hodge numbers modulo an integer. https://doi.org/10.2140/ant.2019.13.2427

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