Multiplicative properties of projectively dual varieties
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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  and its dual version.
KeywordsProjective Space Hessian Matrix Dual Variety Smooth Point Orthogonal Subspace
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- 4.Katz, N.: Pincreaux de Lefschetz; Theoreme d'existence. SGA 7, Springer Lecture Notes340, 212–253Google Scholar