We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham e-Theses
You are in:

On the geometry of rank two vector bundles and two-theta divisors on a curve

Scataglini, Giovanna (2003) On the geometry of rank two vector bundles and two-theta divisors on a curve. Doctoral thesis, Durham University.



This thesis aims at presenting results and remarks concerning the study of subvarieties of the projective space |2Ɵ| associated to a smooth projective curve C of genus at least 3 and its connections to the moduli space SU(_c)(2) of rank 2 semi-stable vector bundles with trivial determinant. In the first part of the thesis, I present a review of Narasimhan and Ramanan's embedding of SU(_C)(2) in |2Ɵ| for non-hyperelliptic curves of genus 3 ([N-R2]). In particular, I clarify some of the points of their construction (2.3.6) and give complete proofs of lemma 5.1 and lemma 5.2 (see 2.3.4 and 2.3.17). Moreover in section 2.3 I show that lemma 5.4 of [N-R2] is false, providing an extensive counterexample (2.4.3).In the second part, I discuss the Abel-Jacobi stratification of |2Ɵ| for non-hyperelliptic curves of genus at least 3 as introduced in [0-P], which generalises classical subvarieties of |2Ɵ| such as the Kummer variety. I show that the top element of these stratifications is always a hypersurface and compute its degree (3.2.5), then I provide insight into the characterisation of the general element of the stratification (§3.3).

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Thesis Date:2003
Copyright:Copyright of this thesis is held by the author
Deposited On:26 Jun 2012 15:21

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitter