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

Remy Van Dobben De Bruyn; Matthias Paulsen

doi:10.1017/fms.2020.48

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

Remy Van Dobben De Bruyn, Matthias Paulsen

Mathematics

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2 Scopus citations

Abstract

Let k be an algebraically closed field of positive characteristic. For any integer <![CDATA[ $m\ge 2$ ]]>, 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.

Original language	English (US)
Article number	e45
Journal	Forum of Mathematics, Sigma
DOIs	https://doi.org/10.1017/fms.2020.48
State	Accepted/In press - 2020

All Science Journal Classification (ASJC) codes

Analysis
Theoretical Computer Science
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1017/fms.2020.48

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title = "The construction problem for Hodge numbers modulo an integer in positive characteristic",

abstract = "Let k be an algebraically closed field of positive characteristic. For any integer <![CDATA[ $m\ge 2$ ]]>, 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.",

author = "{Van Dobben De Bruyn}, Remy and Matthias Paulsen",

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PY - 2020

Y1 - 2020

N2 - Let k be an algebraically closed field of positive characteristic. For any integer <![CDATA[ $m\ge 2$ ]]>, 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.

AB - Let k be an algebraically closed field of positive characteristic. For any integer <![CDATA[ $m\ge 2$ ]]>, 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.

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DO - 10.1017/fms.2020.48

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JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

M1 - e45

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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