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摘要翻译：
维数为d且Picard数为rho(X)的q-阶乘Gorenstein toric Fano变体X对应于顶点为rho(X)+d的单纯自反d-多边形。Casagrande证明了任何单纯自反d多面体至多有3d顶点，如果d是偶数，则分别有3d-1顶点，如果d是奇数。此外，已知d的相等性甚至蕴涵着唯一性直至单模等价性。本文对所有具有3d-1顶点的单纯自反D-多边形进行了完全分类，对应于Picard数为2d-1的D-维q-阶乘Gorenstein toric Fano簇。对于d偶数，存在三个这样的变体，其中两个是奇异的；而对于d奇数(d>1),精确地存在两个，它们都是射影线上的非奇异的扭转纤维束。这概括了第二作者最近的工作。
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英文标题：
《Q-factorial Gorenstein toric Fano varieties with large Picard number》
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作者：
Benjamin Nill, Mikkel {\O}bro
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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英文摘要：
Q-factorial Gorenstein toric Fano varieties X of dimension d with Picard number rho(X) correspond to simplicial reflexive d-polytopes with rho(X)+d vertices. Casagrande showed that any simplicial reflexive d-polytope has at most 3d vertices, if d is even, respectively, 3d-1, if d is odd. Moreover, it is known that equality for d even implies uniqueness up to unimodular equivalence. In this paper we completely classify all simplicial reflexive d-polytopes having 3d-1 vertices, corresponding to d-dimensional Q-factorial Gorenstein toric Fano varieties with Picard number 2d-1. For d even, there exist three such varieties, with two being singular, while for d odd (d > 1) there exist precisely two, both being nonsingular toric fiber bundles over the projective line. This generalizes recent work of the second author.
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PDF链接：
https://arxiv.org/pdf/0805.4533
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