Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.550085
Title: Moduli of symplectic bundles over curves
Author: Hitching, George H.
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 2005
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Abstract:
Let Х be a complex projective smooth irreducible curve of genus g. We begin by giving background material on symplectic vector bundles and principal bundles over X and introduce the moduli spaces we will be studying, In Chapter 2 we describe the stable singular locus and semistable boundary of the moduli space Mx(Sp2 C) of semistable principal Sp2 C-bundles over X. In Chapter 3 we give results on symplectic extensions and Lagrangian subbundles. In Chapter 4, we assemble some results on vector bundles of rank 2 and degree 1 over a curve of genus 2, which are needed in what follows. Chapter 5 describes a generically finite cover of Aix(Sp2C) for a curve of genus 2. In the last chapter, we give some results on theta-divisors of rank 4 symplectic vector bundles over curves: we prove that the general such bundle over a curve of genus 2 possesses a theta-divisor, and characterise those stable bundles with singular theta-divisors. Many results on symplectic bundles admit analogues in the orthogonal case, which we have outlined where possible.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.550085  DOI: Not available
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