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

Part of: (Co)homology theory Algebraic geometry: Foundations Arithmetic problems. Diophantine geometry Birational geometry

Published online by Cambridge University Press:  09 November 2020

Remy van Dobben de Bruyn  and
Matthias Paulsen
Remy van Dobben de Bruyn
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA; E-mail: rdobben@math.princeton.edu Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA
Matthias Paulsen
Affiliation:
Institute of Algebraic Geometry, Gottfried Wilhelm Leibniz Universität Hannover, Welfengarten 1, D-30167Hannover, Germany; E-mail: paulsen@math.uni-hannover.de

Abstract

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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 values modulo m, subject only to Serre duality. In particular, there are no non-trivial polynomial relations between the Hodge numbers.

MSC classification

Primary: 14F99: None of the above, but in this section
Secondary: 14G17: Positive characteristic ground fields 14A10: Varieties and morphisms 14E99: None of the above, but in this section
Type
Algebraic and Complex Geometry
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e45
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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