# The construction problem for Hodge numbers modulo an integer

@article{Paulsen2019TheCP, title={The construction problem for Hodge numbers modulo an integer}, author={Matthias Paulsen and S. Schreieder}, journal={Algebra \& Number Theory}, year={2019}, volume={13}, pages={2427-2434} }

For any integer m ≥ 2 and any dimension n ≥ 1, we show that any ndimensional 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.

#### 3 Citations

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

- Mathematics
- Forum of Mathematics, Sigma
- 2020

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… Expand

On linear relations between cohomological invariants of compact complex manifolds

- Mathematics
- 2021

Roughly speaking, the answer for all three questions is: ‘Only the expected ones’. The third question was famously asked by Hirzebruch [16]. The version of this question concerning the Chern numbers… Expand

The Hodge ring of varieties in positive characteristic

- Mathematics
- 2020

Let $k$ be a field of positive characteristic. We prove that the only linear relations between the Hodge numbers $h^{i,j}(X) = \dim H^j(X,\Omega_X^i)$ that hold for every smooth proper variety $X$… Expand

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

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