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Any algebraic variety in positive characteristic admits a projective model with an inseparable Gauss map. (English) Zbl 1177.14092
Summary: We determine the values attained by the rank of the Gauss map of a projective model for a fixed algebraic variety in positive characteristic \(p\). In particular, it is shown that any variety in \(p>0\) has a projective model such that the differential of the Gauss map is identically zero. On the other hand, we prove that there exists a product of two or more projective spaces admitting an embedding into a projective space such that the differential of the Gauss map is identically zero if and only if \(p=2\).

MSC:
14N05 Projective techniques in algebraic geometry
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