论文标题
正面特征的休眠操作和高斯图
Dormant opers and Gauss maps in positive characteristic
论文作者
论文摘要
给定投影品种的高斯地图是理性地图，该地图在该点向切线空间传递了一个平稳的点，被视为格拉斯曼品种的点。本文的目的是通过H. kaji在正面特征的高斯图上概括结果，并与休眠操作的研究以及Frobenius-Projective结构建立相互作用。首先，我们证明了在平滑的投影品种$ x $上休眠的opers和从$ x $中的封闭的沉浸式的对应关系，并带有纯粹是不可分割的高斯地图的投影空间。通过使用此功能，我们确定高斯图引起的正特征中平滑曲线功能场的子场。此外，该对应关系为我们提供了Fermat Hypersurface上的Frobenius-Progentive结构。该示例体现了阳性特征中代数几何形状的异国情调现象。
The Gauss map of a given projective variety is the rational map that sends a smooth point to the tangent space at that point, considered as a point of the Grassmann variety. The present paper aims to generalize a result by H. Kaji on Gauss maps in positive characteristic and establish an interaction with the study of dormant opers, as well as Frobenius-projective structures. We first prove a correspondence between dormant opers on a smooth projective variety $X$ and closed immersions from $X$ into a projective space with purely inseparable Gauss map. By using this, we determine the subfields of the function field of a smooth curve in positive characteristic induced by Gauss maps. Moreover, the correspondence gives us a Frobenius-projective structure on a Fermat hypersurface. This example embodies an exotic phenomenon of algebraic geometry in positive characteristic.
