Moduli of unstable objects in algebraic geometry

Abstract: The construction of the moduli spaces of stable curves of fixed genus is one of the classical applications of Mumford's geometric invariant theory (GIT), developed in the 1960s; many other moduli spaces of 'stable' objects can be constructed using GIT, as well as in other ways. The aim of this talk is to explain how recent methods from a version of GIT for non-reductive group actions can help us to use suitable 'stability conditions' to stratify moduli stacks into locally closed strata such that not only the open 'stable' strata but also the 'unstable' strata have coarse moduli spaces. In the case of moduli stacks of bundles over a nonsingular projective curve, these stratifications refine the stratification by Harder-Narasimhan type. The talk is based on joint work with Gergely Berczi, Vicky Hoskins and Joshua Jackson.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

The seminar takes place on Tuesdays and Thursdays via Zoom. Zoom passwords are given via mailing list on Fridays. To join the mailing list go to the website.

If you use a calendar system, you can see the individual seminars at bit.ly/zag-seminar-calendar

Times vary to accommodate speakers time zones but times will be announced in GMT time.