A Gauge-Theoretic Approach to the Chern Form of the Canonical Bundle on the Moduli Space of Stable Parabolic Bundles

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dc.contributor.advisorWentworth, Richard Aen_US
dc.contributor.authorTian, Boen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2020-09-25T05:36:31Z
dc.date.available2020-09-25T05:36:31Z
dc.date.issued2020en_US
dc.description.abstractIn this thesis we apply a gauge-theoretic approach to construct the moduli space of stable parabolic bundles on a closed Riemann surface using weighted Sobolev spaces. We study the metric properties of the moduli space, and in particular, we compute the L2 curvature of its canonical bundle. By identifying the canonical bundle with the index bundle of a suitable family of Dolbeault operators, we define a spectral Quillen metric on the canonical bundle via a relative analytic torsion construction first introduced by Müller. We compute the curvature of the canonical bundle with respect to this Quillen metric and find that it consists of the standard Atiyah-Singer term along with a cuspidal contribution coming from the parabolic structure and depending upon the parabolic weights. This gives a new proof of a result of Zograf-Takhtajan.en_US
dc.identifierhttps://doi.org/10.13016/g6ur-y6zv
dc.identifier.urihttp://hdl.handle.net/1903/26449
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledChern formen_US
dc.subject.pquncontrolledCurvatureen_US
dc.subject.pquncontrolledModuli spaceen_US
dc.subject.pquncontrolledParabolic bundleen_US
dc.subject.pquncontrolledQuillen metricen_US
dc.subject.pquncontrolledRelative determinanten_US
dc.titleA Gauge-Theoretic Approach to the Chern Form of the Canonical Bundle on the Moduli Space of Stable Parabolic Bundlesen_US
dc.typeDissertationen_US

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