Hypersurfaces with degenerate duals and the Geometric Complexity Theory Program Academic Article

abstract

• We determine set-theoretic defining equations for the variety Dualk;d;N P.SdCN/ of hypersurfaces of degree d in CN that have dual variety of dimension at most k. We apply these equations to the Mulmuley-Sohoni variety GLn2 OEdetn P.SnCn2 /, showing it is an irreducible component of the variety of hypersurfaces of degree n inCn2 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. Swiss Mathematical Society.

authors

• Landsberg, Joseph

published proceedings

• COMMENTARII MATHEMATICI HELVETICI

author list (cited authors)

• Landsberg, J. M., Manivel, L., & Ressayre, N.

citation count

• 22

complete list of authors

• Landsberg, Joseph M||Manivel, Laurent||Ressayre, Nicolas

publication date

• July 2013

publisher

• European Mathematical Society - EMS - Publishing House GmbH  Publisher

published in

• Commentarii Mathematici Helvetici  Journal

keywords

• Determinant
• Dual Variety
• Geometric Complexity Theory
• Permanent

Digital Object Identifier (DOI)

• 10.4171/CMH/292

start page

• 469

end page

• 484

volume

• 88

issue

• 2

URL

• http://dx.doi.org/10.4171/cmh/292