Hypersurfaces with degenerate duals and the Geometric Complexity Theory Program
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.
Domaines
Géométrie algébrique [math.AG]
Origine : Fichiers produits par l'(les) auteur(s)