Document Zbl 0715.14042 - zbMATH Open
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Projectively dual varieties and hyperdeterminants. (English. Russian original) Zbl 0715.14042
One studies conditions under which the dual variety \(X^{\vee}\) to a projective variety \(X\subset {\mathbb{P}}^ n\) (X linearly normal and nondegenerated) has codimension 1; in this case one considers the question of finding the degree (or the equation) of \(X^{\vee}\). There are considered the cases: (1) \(X\) is the projectivization of the orbit of the highest weight vector in an irreducible representation of a semisimple complex Lie group, (2) \(X\) is a product of projective spaces, embedded by the Segre map.