Pure codimensionality of wobbly bundles

Abstract: Higgs bundles on smooth projective curves were introduced by Hitchin as solutions to gauge equations motivated by physics. They can be seen as points of $T^*N$, where N is the moduli space of vector bundles on the curve. The topology of the moduli space of Higgs bundles is determined by the nilpotent cone, which is a reducible scheme containing the zero section of $T^*N\dashrightarrow N$. Inside this section, wobbly bundles are particularly important, as this is the locus where any other component intersects $N$. In fact, this implies that the geometry of the nilpotent cone can be described in terms of wobbly bundles. In this talk I will explain an inductive method to prove pure codimensionality of the wobbly locus, as announced in a paper by Laumon from the 80's. We expect our method to yield moreover a description of the irreducible components of the nilpotent cone in arbitrary rank.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides )

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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

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