Abelianisation of Meromorphic Connections

Abstract: There is a natural 1-1 correspondence between Higgs bundles on a compact complex curve and line bundles on an appropriate branched cover. This abelianisation process goes through the direct image functor and it has been fruitful in addressing a variety of problems relating to bundles on curves. We extend this abelianisation correspondence from Higgs bundles to flat bundles. This generalisation involves choosing a certain graph which translates to cohomology as a natural cocycle that exhibits a local deformation of the direct image functor. Furthermore, our abelianisation correspondence extends to lambda-connections and recovers the abelianisation of Higgs bundles as lambda goes to 0. Based in part on joint work in progress with Marco Gualtieri.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html