Gauss maps with nontrivial separable degree in positive characteristic

For a projective variety of dimension n in a projective space P-N defined o ver an algebraically closed field, the Gauss map is the rational map of the variety to the Grassmannian of n-planes in P-N, mapping a smooth point to the embedded tangent space to the variety at the point. The purpose here is to give three examples of Gauss maps with separable degrees greater than o ne onto their images in positive characteristic: (1) a smooth variety with Kodaira dimension kappa < n; (2) a normal variety of general type with only isolated singularities; (3) P-n, whose image of the Gauss map is a normal variety of general type. (C) 2001 Elsevier Science B.V. All rights reserved . MSG: 14N05; 14B25.