Algebraic Geometry Seminar
Nicholas Addington
University of Oregon
Moduli spaces of sheaves on moduli spaces of sheaves
Abstract: It often happens that if M is a moduli space of vector bundles on a curve
C, then C is also a moduli space of vector bundles on M, where the bundles
on M come from taking "wrong-way slices" of the the universal bundle on M
x C. This story starts in the '70s and is due to Narasimhan and Ramanan,
Newstead, and others. Reede and Zhang recently observed that a similar
result holds for Hilbert schemes of points on surfaces, and for certain
moduli spaces of rank-0 sheaves on K3 surfaces. I will discuss joint work
with my student Andrew Wray, showing that it holds for moduli spaces of
high-rank sheaves on K3 surfaces. Techniques include the Quillen metric
on determinant line bundles and twistor families of hyperkaehler
manifolds.
Monday January 25, 2021 at 3:00 PM in Zoom