Ritvik Ramkumar : Blowups of scrolls and their degenerations

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

Nov. 28, 2022, 1:30 p.m.

In

636 SEO

Abstract

It is a classical, but also difficult, problem to determine the defining equations of the blowup of P^n along a given subvariety X. In this talk, I will focus on the cases where X is defined by the ideal of maximal minors of a 2xn matrix of linear forms. I will explain how to determine the defining equations and the singularities of their blowup algebras. This relies on a stratification of the Hilbert scheme of determinantal ideals and the combinatorics of square-free degenerations. This is joint work with Alessio Sammartano.