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Title: An arithmetic Bernstein-Kushnirenko inequality
Author: Martínez, César
Sombra, Martín
Keywords: Geometria algebraica
Varietats tòriques
Funcions convexes
Algebraic geometry
Toric varieties
Convex functions
Issue Date: 6-Sep-2018
Publisher: Springer Verlag
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.
Note: Versió postprint del document publicat a:
It is part of: Mathematische Zeitschrift, 2018, vol. 291, p. 1211-1244
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ISSN: 0025-5874
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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