The Michigan Mathematical Journal
- Michigan Math. J.
- Volume 68, Issue 3 (2019), 483-503.
On Separable Higher Gauss Maps
We study the th Gauss map in the sense of F. L. Zak of a projective variety over an algebraically closed field in any characteristic. For all integers with , we show that the contact locus on of a general tangent -plane is a linear variety if the th Gauss map is separable. We also show that for smooth with , the th Gauss map is birational if it is separable, unless is the Segre embedding . This is related to Ein’s classification of varieties with small dual varieties in characteristic zero.
Michigan Math. J., Volume 68, Issue 3 (2019), 483-503.
Received: 24 June 2017
Revised: 30 October 2017
First available in Project Euclid: 18 April 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 14N05: Projective techniques [See also 51N35]
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