Hypertoric varieties and zonotopal tilings
Hypertoric varieties and zonotopal tilings
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Hypertoric 品种和 zonotopal 平铺
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
N. Proudfoot
中科院分区：
文献类型：
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作者：
Matthew B. Arbo;N. Proudfoot
我们给出了过度变化的抽象定义，概括了现有的建设性定义。我们构建了一个与任何带状平铺相关的超张变体，并且我们证明了先前已知的例子正是与常规平铺相关的那些变体。特别是，我们用不规则瓷砖构建的例子以前从未出现过。我们推测我们的构建给出了超曲面变体的完整分类，类似于扇形对复曲面变体的分类。
We give an abstract definition of a hypertoric variety, generalizing the existing constructive definition. We construct a hypertoric variety associated with any zonotopal tiling, and we show that the previously known examples are exactly those varieties associated with regular tilings. In particular, the examples that we construct from irregular tilings have not appeared before. We conjecture that our construction gives a complete classification of hypertoric varieties, analogous to the classification of toric varieties by fans.