We determine set-theoretic defining equations for the variety of hypersurfaces of degree in that have dual variety of dimension at most . We apply these equations to the Mulmuley–Sohoni variety , showing it is an irreducible component of the variety of hypersurfaces of degree in with dual of dimension at most . We establish additional geometric properties of the Mulmuley–Sohoni variety and prove a quadratic lower bound for the determinantal border-complexity of the permanent.
Cite this article
Laurent Manivel, Joseph M. Landsberg, Nicolas Ressayre, Hypersurfaces with degenerate duals and the Geometric Complexity Theory Program. Comment. Math. Helv. 88 (2013), no. 2, pp. 469–484DOI 10.4171/CMH/292