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

Satoru Fukasawa, Hajime Kaji

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 languageEnglish
Pages (from-to)699-703
Number of pages5
JournalMathematische Zeitschrift
Volume256
Issue number4
DOIs
Publication statusPublished - 2007 Aug 1

Keywords

  • Gauss map
  • Reflexive
  • Separable

ASJC Scopus subject areas

  • Mathematics(all)

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