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 2 and any dimension n 1, we show that any n-dimensional Hodge diamond with values in m 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
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