Classification of Gorenstein Toric Del Pezzo Varieties in arbitrary dimension
Classification of Gorenstein Toric Del Pezzo Varieties in arbitrary dimension
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Gorenstein Toric Del Pezzo 品种任意维度的分类
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Dorothee Juny
中科院分区：
文献类型：
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作者：
V. Batyrev;Dorothee Juny
一个n维Gorenstein复曲面Fano簇X称为Del Pezzo簇，如果反正则类K_X是一个Cartier因子的（n-1）$-倍数.我们的目的是给出任意维数$n geq 2$上Gorenstein环面Del Pezzo簇的一个完全的双正则分类。我们表明，同构存在37 Gorenstein环面德尔佩佐品种的尺寸$n$，这不是锥超过$（n-1）$维Gorenstein环面德尔佩佐品种。我们的结果是密切相关的分类的所有Minkowski和分解的自反多边形由于Emiris和Tsigaridas和分类的变形$n$维几乎Del Pezzo流形获得的Jahnke和Peternell。
A $n$-dimensional Gorenstein toric Fano variety $X$ is called Del Pezzo variety if the anticanonical class $-K_X$ is a $(n-1)$-multiple of a Cartier divisor. Our purpose is to give a complete biregular classfication of Gorenstein toric Del Pezzo varieties in arbitrary dimension $n geq 2$. We show that up to isomorphism there exist exactly 37 Gorenstein toric Del Pezzo varieties of dimension $n$ which are not cones over $(n-1)$-dimensional Gorenstein toric Del Pezzo varieties. Our results are closely related to the classification of all Minkowski sum decompositions of reflexive polygons due to Emiris and Tsigaridas and to the classification up to deformation of $n$-dimensional almost Del Pezzo manifolds obtained by Jahnke and Peternell.