Waring problems and the Lefschetz properties

Abstract: We study three variations of the Waring problem for homogeneous polynomials, concerning the Waring rank, the border rank and the cactus rank of a form. We show how the Lefschetz properties of the associated algebra affect them. The main tool is the theory of mixed Hessians and Macaulay-Matlis duality. We construct new families of wild forms, that is, forms whose cactus rank, of schematic nature, is bigger than the border rank, defined geometrically. (Joint with T. Dias, UFRPE)

Mathematics

Audience: researchers in the discipline

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