Speaker
Jarek Buczynski
(IMPAN Warsaw)
Description
The cactus variety of a projective variety X is a version of the secant variety, where we take into account the linear spans of all finite subschemes of bounded length, not only the smooth ones or smoothable ones. I will discuss the definitions and basic properties of cactus rank and cactus varieties, with a particular focus on why they are relevant as an obstruction to study secant varieties. I will also explain the what is the Hilbert scheme of points and what we know about its components. Finally I will relate the components of the cactus variety (typically, one of these components would be the secant variety) to components of Hilbert scheme.
