On the Duals of Segre Varieties

研究成果: Article

9 被引用数 (Scopus)

抄録

The reflexivity, the (semi-)ordinariness, the dimension of dual varieties and the structure of Gauss maps are discussed for Segre varieties, where a Segre variety is the image of the product of two or more projective spaces under Segre embedding. A generalization is given to a theorem of A. Hefez and A. Thorup on Segre varieties of two projective spaces. In particular, a new proof is given to a theorem of F. Knop, G. Menzel, I. M. Gelfand, M. M. Kapranov and A. V. Zelevinsky that states a necessary and sufficient condition for Segre varieties to have codimension one duals. On the other hand, a negative answer is given to a problem raised by S. Kleiman and R. Piene as follows: For a projective variety of dimension at least two, do the Gauss map and the natural projection from the conormal variety to the dual variety have the same inseparable degree?

本文言語English
ページ(範囲)221-229
ページ数9
ジャーナルGeometriae Dedicata
99
1
DOI
出版ステータスPublished - 2003 6 1

ASJC Scopus subject areas

  • Geometry and Topology

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