Mathematics Colloquia and Seminars

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Catalecticant matrices are a common generalization of Hankel matrices and generic symmetric matrices. Their ideals of minors give (some) equations for the secant varieties to Veronese embeddings of projective space. Inspired by a connection between catalecticant matrices and Gorenstein Artin algebras, Geramita conjectured that the 3x3 minors of the "middle'' catalecticants are all equal, and that they generate the ideal of the secant line variety to the Veronese variety. I will introduce a polarization technique that's fundamental for the proof of Geramita's conjecture, and I will describe the decomposition of the coordinate ring of the secant line variety to the Veronese variety as a sum of irreducible representations.