The projective moduli variety [Sscr ][Uscr ]C(2)
of semistable rank 2 vector bundles with
trivial determinant on a smooth projective curve C comes with
a natural morphism
ϕ to the linear series [mid ]2×Θ[mid ] where Θ is the theta
divisor on the Jacobian of C. Well-
known results of Narasimhan and Ramanan say that ϕ is an isomorphism
to
P3 if C
has genus 2 [16], and when C is nonhyperelliptic
of
genus 3 it is an isomorphism to a special Heisenberg-invariant quartic
QC⊂P7 [18].
The present paper is an attempt
to extend these results to higher genus.