Gauss maps with nontrivial separable degree in positive characteristic
Gauss maps with nontrivial separable degree in positive characteristic
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具有正特征的非平凡可分度的高斯图
DOI：
10.1016/s0022-4049(99)00118-8
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发表时间：
2001
影响因子：
0.8
通讯作者：
A. Noma
中科院分区：
文献类型：
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作者：
A. Noma
对于定义在代数闭域上的射影空间PN中的n维射影簇，高斯映射是该簇到PN中n个平面的格拉斯曼的有理映射，将光滑点映射到该点处的簇的嵌入切空间。本文给出了三个可离度大于1的高斯映射到其正特征像上的例子：（1）科代拉维数为κ<n的光滑簇;（2）只具有孤立奇点的一般型正规簇;（3）Pn，其高斯映射的像是一般型正规簇.
For a projective variety of dimension n in a projective space PNdefined over an algebraically closed field, the Gauss map is the rational map of the variety to the Grassmannian of n-planes in PN, mapping a smooth point to the embedded tangent space to the variety at the point. The purpose here is to give three examples of Gauss maps with separable degrees greater than one onto their images in positive characteristic: (1) a smooth variety with Kodaira dimension κ<n; (2) a normal variety of general type with only isolated singularities; (3) Pn, whose image of the Gauss map is a normal variety of general type.