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 ℙN to re-embed into some projective space ℙM 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 ℙN is identically zero; hence the projective variety X re-embedded in ℙM 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 ℙN with suitable degree in positive characteristic is known to satisfy the assumption above. We give some new, other examples of X in ℙN satisfying the assumption.
本文言語 | English |
---|---|
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)