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2018 Heights of hypersurfaces in toric varieties
Roberto Gualdi
Algebra Number Theory 12(10): 2403-2443 (2018). DOI: 10.2140/ant.2018.12.2403

Abstract

For a cycle of codimension 1 in a toric variety, its degree with respect to a nef toric divisor can be understood in terms of the mixed volume of the polytopes associated to the divisor and to the cycle. We prove here that an analogous combinatorial formula holds in the arithmetic setting: the global height of a 1-codimensional cycle with respect to a toric divisor equipped with a semipositive toric metric can be expressed in terms of mixed integrals of the v-adic roof functions associated to the metric and the Legendre–Fenchel dual of the v-adic Ronkin function of the Laurent polynomial of the cycle.

Citation

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Roberto Gualdi. "Heights of hypersurfaces in toric varieties." Algebra Number Theory 12 (10) 2403 - 2443, 2018. https://doi.org/10.2140/ant.2018.12.2403

Information

Received: 14 November 2017; Revised: 16 July 2018; Accepted: 23 September 2018; Published: 2018
First available in Project Euclid: 14 February 2019

zbMATH: 07026822
MathSciNet: MR3911135
Digital Object Identifier: 10.2140/ant.2018.12.2403

Subjects:
Primary: 14M25
Secondary: 11G50, 14G40, 52A39

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.12 • No. 10 • 2018
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