Fall 2014

Cactus Varieties of Cubic Forms: Apolar Local Artinian Gorenstein Rings

Thursday, November 13th, 2014 10:20 am11:10 am

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The rank of a symmetric form is the length of its shortest decomposition as a sum of pure powers of linear forms, i.e. the shortest smooth apolar scheme.

The cactus rank of the form is the the length of the shortest apolar scheme.

The a-th cactus variety of cubic forms C_{a,n} is the closure of the family of cubic forms of cactus rank a in the projective space of cubic forms in n+1 variables.

Together with Ranestad I shall report on recent work with Jelisiejew and Marques giving the dimension and a geometric characterization of the general member of C_{a,n}, when 1\leq a\leq 2n+2.