The separability of the Gauss map and the reflexivity for a projective surface

Satoru Fukasawa*, Hajime Kaji

*この研究の対応する著者

研究成果査読

7 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)699-703
ページ数5
ジャーナルMathematische Zeitschrift
256
4
DOI
出版ステータスPublished - 2007 8 1

ASJC Scopus subject areas

  • 数学 (全般)

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