Duality with expanding maps and shrinking maps, and its applications to Gauss maps
Duality with expanding maps and shrinking maps, and its applications to Gauss maps
复制标题
扩展映射和收缩映射的对偶性及其在高斯映射中的应用
DOI：
10.1007/s00208-013-0965-7
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发表时间：
2014
影响因子：
1.4
通讯作者：
Katsuhisa Furukawa
中科院分区：
文献类型：
--
作者：
Katsuhisa Furukawa;Katsuhisa Furukawa
研究了Grassmann簇的子簇在任意特征下的扩张映射和收缩映射。收缩映射是由兰茨贝格和Piontkowski独立研究的，以刻画高斯图像。为了发展他们的方法，我们引入了扩张映射，它是收缩映射的对偶概念，是高斯映射的推广。然后给出了可分Gauss映射及其象的一个刻划，得到了以下几个问题的结果：（1）可分Gauss映射的一般纤维的线性性;（2）Gauss象刻划的推广;（3）可展簇中线性子簇的一维参数空间的对偶性.
We study expanding maps and shrinking maps of subvarieties of Grassmann varieties in arbitrary characteristic. The shrinking map was studied independently by Landsberg and Piontkowski in order to characterize Gauss images. To develop their method, we introduce the expanding map, which is a dual notion of the shrinking map and is a generalization of the Gauss map. Then we give a characterization of separable Gauss maps and their images, which yields results for the following topics: (1) Linearity of general fibers of separable Gauss maps; (2) Generalization of the characterization of Gauss images; (3) Duality on one-dimensional parameter spaces of linear subvarieties lying in developable varieties.