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A geometric model for weight variations and wall-crossing on moduli spaces of parabolic Higgs bundles over the Riemann sphere

Claudio Meneses

Montag, 23. November 2020 16:15Uhr

In this talk I will describe an ongoing project that aims to reconstruct the hyperkähler geometry of Hitchin metrics on moduli spaces of parabolic Higgs bundles over the Riemann sphere in terms of explicit geometric models. By definition, these moduli spaces depend on a polytope of real parameters called parabolic weights. This dependence induces wall-crossing phenomena, whose incarnation in the models is structurally analogous to a problem of variation of non-reductive GIT-quotients as introduced by Berczi-Jackson-Kirwan. In the smallest possible dimension, these ideas are suited to study the hyperkähler geometry of gravitational instantons of ALG type in terms of the work of Fredrickson–Mazzeo–Swoboda–Weiss.