Hitching, George H. (2005) Moduli of symplectic bundles over curves. Doctoral thesis, Durham University.
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.
|Item Type:||Thesis (Doctoral)|
|Award:||Doctor of Philosophy|
|Copyright:||Copyright of this thesis is held by the author|
|Deposited On:||08 Sep 2011 18:30|