Abstract
For a projective variety of dimension n in a projective space P N defined over 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 one onto their images in positive characteristic: (1) a smooth variety with Kodaira dimension κ< 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.
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