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2018-09-06

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/168539

An arithmetic Bernstein-Kushnirenko inequality

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https://doi.org/10.1007/s00209-018-2107-0

Abstract

We present an upper bound for the height of the isolated zeros in the torus of a system of Laurent polynomials over an adelic field satisfying the product formula. This upper bound is expressed in terms of the mixed integrals of the local roof functions associated to the chosen height function and to the system of Laurent polynomials. We also show that this bound is close to optimal in some families of examples. This result is an arithmetic analogue of the classical Bern¿tein-Ku¿nirenko theorem. Its proof is based on arithmetic intersection theory on toric varieties.

Subject

Geometria algebraica, Varietats tòriques, Funcions convexes

Subject (English)

Algebraic geometry, Toric varieties, Convex functions

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

MARTÍNEZ, César and SOMBRA, Martín. An arithmetic Bernstein-Kushnirenko inequality. Mathematische Zeitschrift. 2018. Vol. 291, num. 1211-1244. ISSN 0025-5874. [consulted: 10 of August of 2026]. Available at: https://hdl.handle.net/2445/168539

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