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