Abstract
It is known that if a projective variety X in P N is reflexive with respect to the projective dual, then the Gauss map of X defined by embedded tangent spaces is separable, and moreover that the converse is not true in general. We prove that the converse holds under the assumption that X is of dimension two. Explaining the subtleness of the problem, we present an example of smooth projective surfaces in arbitrary positive characteristic, which gives a negative answer to a question raised by S. Kleiman and R. Piene on the inseparability of the Gauss map.
Original language | English |
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Pages (from-to) | 699-703 |
Number of pages | 5 |
Journal | Mathematische Zeitschrift |
Volume | 256 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2007 Aug |
Keywords
- Gauss map
- Reflexive
- Separable
ASJC Scopus subject areas
- Mathematics(all)