# 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}
}
• Published 2019
• Mathematics
• Algebra & Number Theory
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 ofExpand
On linear relations between cohomological invariants of compact complex manifolds
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 numbersExpand
The Hodge ring of varieties in positive characteristic
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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