Sep 27 2021

Algebraic Geometry Seminar: Rational singularities of nested Hilbert schemes, by Ritvik Ramkumar

September 27, 2021

3:00 PM - 3:50 PM




Chicago, IL

Ritvik Ramkumar (UC Berkeley): Rational singularities of nested Hilbert schemes

For a smooth surface S the Hilbert scheme of points S^(n) is a well studied smooth parameter space. In this talk I will consider a natural generalization, the nested Hilbert scheme of points S^(n,m) which parameterizes pairs of subschemes X \supseteq Y of S with deg(X) = n and deg(Y) = m. In contrast to the usual Hilbert scheme of points, S^(n,m) is almost always singular and it is known that S(n,1) has rational singularities. I will discuss some general techniques to study S^(n,m) and apply them to show that S^(n,2) also has rational singularities. This relies on a connection between S^(n,2) and a certain variety of matrices, and involves square-free Gröbner degenerations as well as the Kempf-Weyman geometric technique. This is joint work with Alessio Sammartano.

Please click here to make changes to, or delete, this seminar announcement.


Izzet Coskun

Date posted

Sep 28, 2021

Date updated

Sep 28, 2021


Ritvik Ramkumar | (UC Berkeley)