2013/10/21 by Katsuhisa Furukawa, Furukawa, Katsuhisa
Mathematics · Physics and Astronomy · #14M15 (Secondary) #14N05 (Primary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:14M15 #msc:14N05
paper · pdf · doi:10.48550/arxiv.1310.5387
8 pages
openalex publication_date 2013/10/21 · arxiv created 2015/06/30 · arxiv updated 2015/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A general fiber of the Gauss map of a projective variety in ℙN coincides with a linear subvariety of ℙN 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.