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摘要翻译：
我们定义了q-正规格多边形。这类多边形的自然例子是严格组合等价格多边形的Cayley和，它们对应于特别好的曲面纤维，即曲面射影束。在最近的一篇论文中，Batyrev和Nill提出了一个界N(d)，使得每一个d度且维数至少为N(d)的格多面体分解为一个Cayley和。对于光滑q-正规多边形，我们给出了这个问题的尖锐回答。证明了当n大于或等于2d+1时，任何维数为n且次为d的光滑q-正规格多面体P是严格组合等价多面体的Cayley和。该证明依赖于对与相应的toric嵌入相关的nef值态射的研究。
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英文标题：
《Classifying smooth lattice polytopes via toric fibrations》
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作者：
Alicia Dickenstein, Sandra Di Rocco, Ragni Piene
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最新提交年份：
2009
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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：
We define Q-normal lattice polytopes. Natural examples of such polytopes are Cayley sums of strictly combinatorially equivalent lattice polytopes, which correspond to particularly nice toric fibrations, namely toric projective bundles. In a recent paper Batyrev and Nill have suggested that there should be a bound, N(d), such that every lattice polytope of degree d and dimension at least N(d) decomposes as a Cayley sum. We give a sharp answer to this question for smooth Q-normal polytopes. We show that any smooth Q-normal lattice polytope P of dimension n and degree d is a Cayley sum of strictly combinatorially equivalent polytopes if n is greater than or equal to 2d+1. The proof relies on the study of the nef value morphism associated to the corresponding toric embedding.
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PDF链接：
https://arxiv.org/pdf/0809.3136
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