An arithmetic Bernstein-Kushnirenko inequality
| Autor: | Martín Sombra, César Martínez |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Kantorovich inequality
Intersection theory medicine.medical_specialty Funcions convexes Convex functions General Mathematics 010102 general mathematics Ky Fan inequality Field (mathematics) Toric varieties Inequality of arithmetic and geometric means 01 natural sciences Upper and lower bounds Algebraic geometry Linear inequality Geometria algebraica 0103 physical sciences medicine 010307 mathematical physics Rearrangement inequality 0101 mathematics Arithmetic Varietats tòriques Mathematics |
| Zdroj: | Dipòsit Digital de la UB Universidad de Barcelona |
| Popis: | 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 Bernstein–Kusnirenko theorem. Its proof is based on arithmetic intersection theory on toric varieties. |
| Databáze: | OpenAIRE |
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