An arithmetic Bernstein-Kushnirenko inequality
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 t...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/168539 |
| Acesso em linha: | https://hdl.handle.net/2445/168539 |
| Access Level: | acceso abierto |
| Palavra-chave: | Geometria algebraica Varietats tòriques Funcions convexes Algebraic geometry Toric varieties Convex functions |
| Resumo: | 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. |
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