Gauss maps of toric varieties
Gauss maps of toric varieties
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DOI：
10.2748/tmj/1505181625
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发表时间：
2014-03
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影响因子：
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通讯作者：
Katsuhisa Furukawa;Atsushi Ito
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作者：
Katsuhisa Furukawa;Atsushi Ito
我们研究高斯映射（不一定正常）投射环面品种在代数闭域的任意特征。主要结果如下：（1）环面簇的Gauss映射的结构可用组合学的任意特征描述。(2)我们给出了复曲面情况下的可展性准则。特别地，我们证明了任何高斯映射退化的复曲面簇必是特征为零的复曲面簇的并。(3)作为应用，我们提供了两个复曲面簇的构造，其高斯映射具有一些给定的数据（例如，纤维，图像）呈阳性特征。
We investigate Gauss maps of (not necessarily normal) projective toric varieties over an algebraically closed field of arbitrary characteristic. The main results are as follows: (1) The structure of the Gauss map of a toric variety is described in terms of combinatorics in any characteristic. (2) We give a developability criterion in the toric case. In particular, we show that any toric variety whose Gauss map is degenerate must be the join of some toric varieties in characteristic zero. (3) As applications, we provide two constructions of toric varieties whose Gauss maps have some given data (e.g., fibers, images) in positive characteristic.