Let X be a complex projective curve which is smooth and irreducible of genus 2. The moduli space 2 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 2 by a family of 5-dimensional projective spaces, and outline some applications
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