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Geometric Analysis Seminar

Construction of the moduli space of Higgs bundles using analytic methods.

Yue Fan, University of Maryland

Location:  via Zoom,
Date & time: Tuesday, 27 October 2020 at 2:50PM - 3:50PM

Abstract: Introduced by Hitchin, a Higgs bundle \((E,\Phi)\) on a complex manifold \(X\) is a holomorphic vector bundle \(E\) together with an \(\End E\)-valued holomorphic 1-form \(\Phi\). The moduli space of Higgs bundles was constructed by Nitsure where \(X\) is a smooth projective curve and by Simpson where \(X\) is a smooth projective variety. They both used Geometric Invariant Theory, and the moduli space is a quasi-projective variety. It is a folklore theorem that the Kuranishi slice method can be used to construct this moduli space as a complex space where \(X\) is a closed Riemann surface. I will present a proof of this folklore theorem and show that the resulting complex space is biholomorphic to the one in the category of schemes. Moreover, I will briefly talk about some applications of this new construction.

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