The Michigan Mathematical Journal

On Separable Higher Gauss Maps

Katsuhisa Furukawa and Atsushi Ito

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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.

Article information

Source
Michigan Math. J., Volume 68, Issue 3 (2019), 483-503.

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

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1555574416

Digital Object Identifier
doi:10.1307/mmj/1555574416

Mathematical Reviews number (MathSciNet)
MR3990168

Subjects
Primary: 14N05: Projective techniques [See also 51N35]

Citation

Furukawa, Katsuhisa; Ito, Atsushi. On Separable Higher Gauss Maps. Michigan Math. J. 68 (2019), no. 3, 483--503. doi:10.1307/mmj/1555574416. https://projecteuclid.org/euclid.mmj/1555574416


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