Mathematische Annalen

, Volume 342, Issue 2, pp 279–289 | Cite as

The reflexivity of a Segre product of projective varieties

  • Satoru Fukasawa
  • Hajime KajiEmail author


We study the reflexivity of a Segre product of a projective space \({\mathbb P^m}\) and a projective variety Y, and give a criterion for \({\mathbb P^m \times Y}\) to be reflexive in terms of m, the dimension of Y, the rank of the general Hessian of Y and the characteristic of the ground field. Our study is closely related to a question raised by Kleiman and Piene on the relationship between the conormal map and the Gauss map.

Mathematics Subject Classification (2000)



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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematics, School of Science and EngineeringWaseda UniversityShinjuku, TokyoJapan

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