An Analytic Construction of the Moduli Space of Higgs Bundles over Riemann Surfaces
| dc.contributor.advisor | Wentworth, Richard RW | en_US |
| dc.contributor.author | Fan, Yue | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2021-07-13T05:31:46Z | |
| dc.date.available | 2021-07-13T05:31:46Z | |
| dc.date.issued | 2021 | en_US |
| dc.description.abstract | The moduli space of Higgs bundles over Riemann surfaces can be defined as a quotient of an infinite-dimensional space by an infinite-dimensional Lie group. In this thesis, we use the Kuranishi slice method to endow this quotient with the struc-ture of a normal complex space. We also give a direct proof that the moduli space is locally modeled on an affine geometric invariant theory quotient of a quadratic cone by a complex reductive group. Moreover, we show that the moduli space admits an orbit type decomposition such that the decomposition is a Whitney stratification, and each stratum has a complex symplectic structure and a Kähler structure. The complex symplectic structures glue to a complex Poisson bracket on the structure sheaf, and the Kähler structures glue to a singular weak Kähler metric on the moduli space. Finally, we use the symplectic cut to show that the moduli space admits a projective compactification and hence is quasi-projective. | en_US |
| dc.identifier | https://doi.org/10.13016/p9er-fryi | |
| dc.identifier.uri | http://hdl.handle.net/1903/27348 | |
| dc.language.iso | en | en_US |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.title | An Analytic Construction of the Moduli Space of Higgs Bundles over Riemann Surfaces | en_US |
| dc.type | Dissertation | en_US |
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