Sep 27 2021

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

September 27, 2021

3:00 PM - 3:50 PM

Location

Zoom

Address

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.

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Contact

Izzet Coskun

Date posted

Sep 28, 2021

Date updated

Sep 28, 2021

Speakers

Ritvik Ramkumar | (UC Berkeley)