On Gauss Maps in Positive Characteristic in View of Images, Fibers, and Field Extensions
On Gauss Maps in Positive Characteristic in View of Images, Fibers, and Field Extensions
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从图像、光纤和场扩展的角度论正特性高斯图
DOI：
10.1093/imrn/rnw080
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发表时间：
2017
影响因子：
1
通讯作者：
Ito Atsushi
中科院分区：
文献类型：
--
作者：
Furukawa Katsuhisa;Ito Atsushi
射影簇的高斯映射是格拉斯曼簇的有理映射。在积极的特征中，我们显示了以下结果。 (1) 对于给定的射影簇and，我们构造一个射影簇，其高斯图为其一般纤维，并为其图像。更一般地，我们对品种族进行这种构建，而不是固定的。 (2) At least in the case when the characteristic is not equal to, any inseparable field extension appears as the extension induced from the Gauss map of some.
The Gauss map of a projective varietyis a rational map fromto a Grassmann variety. In positive characteristic, we show the following results. (1) For given projective varietiesand, we construct a projective varietywhose Gauss map hasas its general fiber and hasas its image. More generally, we give such construction for families of varieties overinstead of fixed. (2) At least in the case when the characteristic is not equal to, any inseparable field extension appears as the extension induced from the Gauss map of some.