A refinement of the Bernstein-Kushnirenlo estimate
| hal.structure.identifier | Institut de Mathématiques de Jussieu [IMJ] | |
| dc.contributor.author | PHILIPPON, Patrice | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | SOMBRA, Martin | |
| dc.date.accessioned | 2024-04-04T02:42:13Z | |
| dc.date.available | 2024-04-04T02:42:13Z | |
| dc.date.issued | 2008 | |
| dc.identifier.issn | 0001-8708 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191224 | |
| dc.description.abstractEn | A theorem of Kushnirenko and Bernshtein shows that the number of isolated roots in the torus of a system of polynomials is bounded above by the mixed volume of the Newton polytopes of the given polynomials, and that this upper bound is generically exact. We improve on this result by introducing refined combinatorial invariants of polynomials and a generalization of the mixed volume of convex bodies: the mixed integral of concave functions. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | System of polynomial equations | |
| dc.subject.en | Newton polytope | |
| dc.subject.en | sup-convolution | |
| dc.subject.en | mixed | |
| dc.subject.en | integral | |
| dc.subject.en | toric variety over a curve | |
| dc.subject.en | mixed degree | |
| dc.subject.en | Chow weight | |
| dc.title.en | A refinement of the Bernstein-Kushnirenlo estimate | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| bordeaux.journal | Advances in Mathematics | |
| bordeaux.page | 1370-1418 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 218 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00358706 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00358706v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Advances%20in%20Mathematics&rft.date=2008&rft.issue=218&rft.spage=1370-1418&rft.epage=1370-1418&rft.eissn=0001-8708&rft.issn=0001-8708&rft.au=PHILIPPON,%20Patrice&SOMBRA,%20Martin&rft.genre=article |
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