## 抄録

We study the relationship between the generic smoothness of the Gauss map and the reflexivity (with respect to the projective dual) for a projective variety defined over an algebraically closed field. The problem we discuss here is whether it is possible for a projective variety X in ℙ^{N} to re-embed into some projective space ℙ^{M} so as to be non-reflexive with generically smooth Gauss map. Our result is that the answer is affirmative under the assumption that X has dimension at least 3 and the differential of the Gauss map of X in ℙ^{N} is identically zero; hence the projective variety X re-embedded in ℙ^{M} yields a negative answer to Kleiman-Piene's question: Does the generic smoothness of the Gauss map imply reflexivity for a projective variety? A Fermat hypersurface in ℙ^{N} with suitable degree in positive characteristic is known to satisfy the assumption above. We give some new, other examples of X in ℙ^{N} satisfying the assumption.

本文言語 | English |
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ページ（範囲） | 1412-1417 |

ページ数 | 6 |

ジャーナル | Mathematische Nachrichten |

巻 | 281 |

号 | 10 |

DOI | |

出版ステータス | Published - 2008 10月 |

## ASJC Scopus subject areas

- 数学 (全般)