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August 2019 On Separable Higher Gauss Maps
Katsuhisa Furukawa, Atsushi Ito
Michigan Math. J. 68(3): 483-503 (August 2019). DOI: 10.1307/mmj/1555574416

Abstract

We study the mth Gauss map in the sense of F. L. Zak of a projective variety XPN over an algebraically closed field in any characteristic. For all integers m with n:=dim(X)m<N, we show that the contact locus on X of a general tangent m-plane is a linear variety if the mth Gauss map is separable. We also show that for smooth X with n<N2, the (n+1)th Gauss map is birational if it is separable, unless X is the Segre embedding P1×PnP2n1. This is related to Ein’s classification of varieties with small dual varieties in characteristic zero.

Citation

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Katsuhisa Furukawa. Atsushi Ito. "On Separable Higher Gauss Maps." Michigan Math. J. 68 (3) 483 - 503, August 2019. https://doi.org/10.1307/mmj/1555574416

Information

Received: 24 June 2017; Revised: 30 October 2017; Published: August 2019
First available in Project Euclid: 18 April 2019

zbMATH: 07130696
MathSciNet: MR3990168
Digital Object Identifier: 10.1307/mmj/1555574416

Subjects:
Primary: 14N05

Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 3 • August 2019
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