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Pré-Publication, Document De Travail Année : 2013

Hypersurfaces with degenerate duals and the Geometric Complexity Theory Program

Laurent Manivel

Résumé

We determine set-theoretic defining equations for the variety of hypersurfaces of degree d in an N-dimensional complex vector space that have dual variety of dimension at most k. We apply these equations to the Mulmuley-Sohoni variety, the GL_{n^2} orbit closure of the determinant, showing it is an irreducible component of the variety of hypersurfaces of degree n in C^{n^2} with dual of dimension at most 2n-2. We establish additional geometric properties of the Mulmuley-Sohoni variety and prove a quadratic lower bound for the determinantal border-complexity of the permanent.
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hal-01250891 , version 1 (12-06-2023)

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Laurent Manivel. Hypersurfaces with degenerate duals and the Geometric Complexity Theory Program. 2023. ⟨hal-01250891⟩
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