Learn More
We determine set-theoretic defining equations for the variety Dual k,d,N ⊂ P(S d C N) of hypersurfaces of degree d in C N that have dual variety of dimension at most k. We apply these equations to the Mulmuley-Sohoni variety GL n 2 · [detn] ⊂ P(S n C n 2), showing it is an irreducible component of the variety of hypersurfaces of degree n in C n 2 with dual(More)
Grenet's determinantal representation for the permanent is optimal among determinantal representations that are equivariant with respect to left multiplication by permutation and diagonal matrices (roughly half the symmetry group of the permanent). In particular, if any optimal determinantal representation of the permanent must be polynomially related to(More)
In [3], Belkale and Kumar define a new product on the cohomology of flag varieties and use this new product to give an improved solution to the eigencone problem for complex reductive groups. In this paper, we give a generalization of the Belkale-Kumar product to the branching Schubert calculus setting. The study of Branching Schubert calculus attempts to(More)
We study deformations of orbit closures for the action of a connected semisimple group G on its Lie algebra g, especially when G is the special linear group. The tools we use are on the one hand the invariant Hilbert scheme and on the other hand the sheets of g. We show that when G is the special linear group, the connected components of the invariant(More)
We initiate a study of determinantal representations with symmetry. We show that Grenet's determinantal representation for the permanent is optimal among determinantal representations respecting left multiplication by permutation and diagonal matrices (roughly half the symmetry group of the permanent). In particular, if any optimal determinantal(More)
Actions des groupes algébriques sur les variétés affines et normalité d'adhérences d'orbites Thèse soutenue publiquement le 10 mai 2011, devant le jury composé de : (et merci pour le vrai café italien!), déjà docteurs : Alvaro, Rodrigo et Alexander, et tous les autres bien sûr ! Je remercie tous le personnel administratif et technique, grâce à qui j'ai pu(More)
  • 1