Algebraic Geometry Seminar

Hilbert schemes of points on surfaces are some of the most classically studied varieties in algebraic geometry and have also proven to be important objects in representation theory, combinatorics, and symplectic geometry. In this talk, I will introduce (nested) Hilbert schemes and cover the relevant background material from birational geometry. Then, I will focus on two results: the computation of the class of Severi divisors in the Hilbert scheme and the computation of the ample cone of the nested Hilbert scheme including an application to syzygies.
Speaker(s): Tim Ryan (Stony Brook)