Abstract:
Inspired by the work of Eisenbud-Koh-Stillman we compare the
r-th secant variety of a Veronese variety (or more generally
Veronese reembedding of a smooth variety) with the zero set
of the (r+1)x (r+1) minors of catalecticats. To do this we
define the r-th cactus variety of a given variety X as a
closure of the sum of linear spans of 0-dimensional
sub-schemes of X. As a result we obtain set-theoretical
equations of the r-th secant for small r or dimension of the
variety and high degree of the Veronese reembedding.

This is a joint work with Jarek Buczyński.

This is a joint work with Jarek Buczyński.