On general fibers of Gauss maps in positive characteristic

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• 作者：Katsuhisa Furukawa ^{katu@tims.ntu.edu.tw" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 14N05 ; secondary ; 14M15
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 April 2016
• 年：2016
• 卷：451
• 期：Complete
• 页码：293-301
• 全文大小：298 K

文摘

A general fiber of the Gauss map of a projective variety in P^N${\mathbb{P}}^N$ coincides with a linear subvariety of P^N${\mathbb{P}}^N$ in characteristic zero. In positive characteristic, S. Fukasawa showed that a general fiber of the Gauss map can be a non-linear variety. In this paper, we show that each irreducible component of such a possibly non-linear fiber of the Gauss map is contracted to one point by the degeneracy map, and is contained in a linear subvariety corresponding to the kernel of the differential of the Gauss map. We also show the inseparability of Gauss maps of strange varieties not being cones.