Convex bodies and algebraic equations on affine varieties
| dc.creator | Kaveh, Kiumars | |
| dc.creator | Khovanskii, Askold G. | |
| dc.date | 2008-04-25 | |
| dc.date.accessioned | 2026-07-07T09:35:19Z | |
| dc.date.available | 2026-07-07T09:35:19Z | |
| dc.description | Given an affine variety X and a finite dimensional vector space of regular functions L on X, we associate a convex body to (X, L) such that its volume is responsible for the number of solutions of a generic system of functions from L. This is a far reaching generalization of usual theory of Newton polytopes (which is concerned with toric varieties). As applications we give new, simple and transparent proofs of some well-known theorems in both algebraic geometry (e.g. Hodge Index Theorem) and convex geometry (e.g. Alexandrov-Fenchel inequality). Our main tools are classical Hilbert theory on degree of subvarieties of a projective space (in algebraic geometry) and Brunn-Minkowski inequality (in convex geometric). | |
| dc.description | Preliminary version, may contain several typos, 44 pages | |
| dc.identifier | https://arxiv.org/abs/0804.4095 | |
| dc.identifier | http://arxiv.org/abs/0804.4095 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159794 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Convex bodies and algebraic equations on affine varieties | |
| dc.type | text |