与面对称多面体相关的光滑Fano环变异的量子上同调的半简单性

Q3 Mathematics

Electronic Research Announcements in Mathematical Sciences Pub Date : 2011-03-03 DOI:10.3934/era.2011.18.131

Benjamin P. Mirabelli, Maksim Maydanskiy

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引用次数: 2

摘要

光滑范诺环辛流形的量子上同调代数的零次部分由其矩多面体的超势函数W决定。特别地，这个代数是半简单的，即分裂为域的乘积，当且仅当W$的所有临界点都是非简并的。在本文中，我们证明了这一非简并性对于所有具有面对称对偶到矩多面体的光滑范诺环变体都成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Semisimplicity of the quantum cohomology for smooth Fano toric varieties associated with facet symmetric polytopes

The degree zero part of the quantum cohomology algebra of a smooth Fano toric symplectic manifold is determined by the superpotential function, $W$, of its moment polytope. In particular, this algebra is semisimple, i.e. splits as a product of fields, if and only if all the critical points of $W$ are non-degenerate. In this paper, we prove that this non-degeneracy holds for all smooth Fano toric varieties with facet-symmetric duals to moment polytopes.

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来源期刊

Electronic Research Announcements in Mathematical Sciences 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication. ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007