Apolarity and decompositions of homogeneous forms

Kristian Ranestad
University of Oslo

Apolarity is a classical, but little used tool in algebraic geometry. I shall discuss its application to the study of power sum decomposition of homogeneous forms and the related notions of rank and cactus rank of form. On the algebraic side the decomposition problem leads to a study of artinian Gorenstein rings, and on the geometric side it leads to a study of higher secant and cactus varieties.

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