### 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 1 |

### Keywords

- Gauss map
- Reflexive
- Separable

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Fukasawa, S., & Kaji, H. (2007). The separability of the Gauss map and the reflexivity for a projective surface.

*Mathematische Zeitschrift*,*256*(4), 699-703. https://doi.org/10.1007/s00209-006-0085-0