School of Mathematics Seminars and Lectures
A stacky approach to identify the semi-stable locus of vector bundles
by Mr. Arkamouli Debnath (TIFR, Mumbai)
Wednesday, May 10, 2023 from to (Asia/Kolkata)
Abstract:This talk is based on the preprint (https://arxiv.org/abs/2302.09245 ) by Dario Weissmann and Xucheng Zhang. It also fits in the framework of the series of papers being written at recent times by mathematicians like Jarod Alper, Jochen Heinloth etc with the idea to rewrite the available literature about moduli spaces in the language of stacks and avoiding GIT. The existence of the course moduli space of semistable vector bundles on a smooth projective curve is a well known result and the classical proof relies on the notion of semi-stable points in GIT. This paper will try to give a stacky criteria to identify the semi-stable sublocus of the stack of vector bundles. One of the main contributions of this paper is to identify when the good/adequate moduli space (as introduced by Alper, which is apriori an algebraic space) becomes a scheme.