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Multiplicative properties of projectively dual varieties

Abstract

We present a general formula for the dimension of the projectively dual of the product of two projective varietiesX 1 andX 2, in terms of dimensions ofX 1,X 2 and their projective duals (Theorem 0.1). The proof is based on the formula due to N. Katz expressing the dimension of the dual variety in terms of the rank of certain Hessian matrix. Some consequences and related results are given, including the “Cayley trick” from [3] and its dual version.

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Partially supported by the NSF (DMS-9102432)

Partially supported by the NSF (DMS-9104867)

This article was processed by the author using the Springer-Verlag TEE mamath macro package 1990.

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Weyman, J., Zelevinsky, A. Multiplicative properties of projectively dual varieties. Manuscripta Math 82, 139–148 (1994). https://doi.org/10.1007/BF02567693

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Keywords

  • Projective Space
  • Hessian Matrix
  • Dual Variety
  • Smooth Point
  • Orthogonal Subspace