#### Vol. 13, No. 10, 2019

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The construction problem for Hodge numbers modulo an integer

### Matthias Paulsen and Stefan Schreieder

Vol. 13 (2019), No. 10, 2427–2434
##### Abstract

For any integer $m\ge 2$ and any dimension $n\ge 1$, 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.

##### Keywords
Hodge numbers, Kähler manifolds, construction problem
##### Mathematical Subject Classification 2010
Primary: 32Q15
Secondary: 14C30, 14E99, 51M15