Abstract
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.
Citation
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