Parabolic Higgs bundles on toric varieties

Martin Ulirsch (Frankfurt)

03-Jun-2021, 12:00-13:00 (3 years ago)

Abstract: In this talk I will explain a version of Simpson’s non-abelian Hodge correspondence on a toric variety X. There is a natural 1-1 correspondence between stable parabolic Higgs bundles on X and irreducible representations of the fundamental group of the big torus. This correspondence reduces to a correspondence between toric vector bundles and integral unitary representations in a suitable sense. In this story the spherical Tits building will have a surprise appearance. The main result suggests (at least to me) that there is a yet-to-be-discovered logarithmic incarnation of the non-abelian Hodge correspondence.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )


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.

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Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
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