Derived categories of moduli of parabolic bundles on a projective line
Organizers
Speaker
Anton Fonarev
Time
Thursday, May 30, 2024 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
There has been a lot of work done recently in the study of the bounded derived categories of moduli spaces of parabolic bundles on curves. Let C be a curve of genus at least two, and let L be a line bundle of odd degree on it. I was observed some time ago that the motive of the moduli space of rank 2 stable vector bundles on C with determinant L decomposes into motives of symmetric powers of this curve. Thus, it is natural to conjecture that the bounded derived category of this moduli space has an analogous semiorthogonal decomposition. The first results in this direction were obtained by Narasimhan and, independently, Kuznetsov and myself: an embedding of the bounded derived category of the curve itself was constructed. This result initiated a series of papers which culminated in the whole decomposition being constructed (the last bit was done by Tevelev who seemingly proved that the corresponding components generate the derived category).
If we pass to genus zero, the theory of vector bundles is rather poor: every vector bundle splits into a direct sum of line bundles; however, there is a reasonable substitute for moduli of stable bundles in theses case — moduli of parabolic bundles. We will give an overview of the higher genus story and ask a similar question about the derived category of certain moduli of rank 2 parabolic bundles on a projective line.
If we pass to genus zero, the theory of vector bundles is rather poor: every vector bundle splits into a direct sum of line bundles; however, there is a reasonable substitute for moduli of stable bundles in theses case — moduli of parabolic bundles. We will give an overview of the higher genus story and ask a similar question about the derived category of certain moduli of rank 2 parabolic bundles on a projective line.