The construction problem for Hodge numbers modulo an integer

Paulsen, Matthias; Schreieder, Stefan

doi:10.2140/ant.2019.13.2427

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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

DOI: 10.2140/ant.2019.13.2427

Abstract

For any integer $m \geq 2$ and any dimension $n \geq 1$ , we show that any $n$ -dimensional Hodge diamond with values in $ℤ ∕ m ℤ$ 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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Keywords

Hodge numbers, Kähler manifolds, construction problem

Mathematical Subject Classification 2010

Primary: 32Q15

Secondary: 14C30, 14E99, 51M15

Milestones

Received: 13 March 2019

Revised: 13 June 2019

Accepted: 29 July 2019

Published: 6 January 2020

Authors

Matthias Paulsen
Mathematisches Institut LMU München Germany

Stefan Schreieder
Mathematisches Institut LMU München Germany

Vol. 13, No. 10, 2019