ONLINE: Introduction to Bridgeland stability

Speaker:

Campbell Wheeler

Organiser(s):

Gaetan Borot, Severin Charbonnier, Alessandro Giacchetto, Reinier Kramer and Campbell Wheeler

Affiliation:

MPIM

Date:

Fri, 17/04/2020 - 16:00 - 17:30

Parent event:

ONLINE Reading group: DT invariants, stability conditions and geometry [2]

Connection via the link: https://conf.dfn.de/webapp/conference/979130115/ [3]
or via the stream: https://www.conf.dfn.de/stream/nr57d2v82ptdr [4]

If you plan to join, please give Gaetan Borot (gborot[at]mpim-bonn.mpg.de) notice
in advance, so that we can make sure all people concerned are there before starting the talk.

Abstract:

We will begin by considering the classification problem for vector bundles on curves over the complex numbers. This leads to classical notions of stability of coherent sheaves on a curve. In essence, we can use stability conditions to decompose the (derived) category of coherent sheaves on a curve into workable pieces. We will then generalise these ideas to any abelian or triangulated category with the (derived) category of coherent sheaves of higher dimensional varieties in mind. We will see that in the case of curves, up to an equivalence, there is a unique stability condition that agrees with the classical one. We will see that the set of stability conditions comes with a natural topology and is in fact a complex manifold.