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, Volume 82, Issue 1, pp 139–148 | Cite as

Multiplicative properties of projectively dual varieties

  • Jerzy Weyman
  • Andrei Zelevinsky


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.


Projective Space Hessian Matrix Dual Variety Smooth Point Orthogonal Subspace 
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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Jerzy Weyman
    • 1
  • Andrei Zelevinsky
    • 1
  1. 1.Department of MathematicsNortheastern UniversityBostonU.S.A.

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