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Journal of the London Mathematical Society Advance Access originally published online on February 2, 2007
Journal of the London Mathematical Society 2007 75(1):255-272; doi:10.1112/jlms/jdl011
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© 2007 London Mathematical Society

Moduli of rank 4 symplectic vector bundles over a curve of genus 2

George H. Hitching

Institut für Algebraische Geometrie
Leibniz Universität Hannover
Welfengarten 1
30167 Hannover
Germany
hitching{at}math.uni-hannover.de

Let X be a complex projective curve which is smooth and irreducible of genus 2. The moduli space M2 of semistable symplectic vector bundles of rank 4 over X is a variety of dimension 10. After assembling some results on vector bundles of rank 2 and odd degree over X, we construct a generically finite cover of M2 by a family of 5-dimensional projective spaces, and outline some applications.

2000 Mathematics Subject Classification 14H60 (primary), 14D20 (secondary).

The author was supported during the writing of this paper by the Engineering and Physical Sciences Research Council, the Universities of Durham and Nice-Sophia-Antipolis and Leibniz Universität Hannover, and the Deutsche Forschungsgemeinschaft Schwerpunktprogramm ‘Globale Methoden in der komplexen Geometrie’.

Received October 24, 2005; revised April 24, 2006; published online February 2, 2007.


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