A structure theorem for SU(2) and the moduli of pointed genus zero curves

Details A structure theorem for SU(2) and the moduli of pointed genus zero curves A structure theorem for SU(2) and the moduli of pointed genus zero curves

2009-03-31

arxiv.org/abs/0903.5515v3

Mathematics

Algebraic Geometry

16 pages, almost final version. Added details and lots of references, corrected inaccuracies and typos

Scientific paper

Let SUC(2) be the moduli space of rank 2 semistable vector bundles with trivial determinant on a smooth complex curve C of genus g > 1,non-hyperellptic if g > 2. In this paper we prove a birational structure theorem for SUC(2) that generalizes that of [Bol07] for genus 2. Notably we give a birational description of SU(2) as a fibration over P^g, where the fibers are GIT compactifications of the moduli space M_{0,2g} of 2g-pointed rational curves. This is done by describing the classifying maps of extensions of the line bundles associated to some effective divisors. In particular, for g = 3 our construction shows that the Coble quartic is birational to a fibration in Segre cubics over a P3.

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