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Heisenberg invariant quartics and [Sscr ][Uscr ]C(2) for a curve of genus four

Published online by Cambridge University Press:  01 January 1999

WILLIAM OXBURY  and
CHRISTIAN PAULY
WILLIAM OXBURY
Affiliation:
Department of Mathematical Sciences, Science Laboratories, South Road, Durham DH1 3LE. e-mail: w.m.oxbury@durham.ac.uk
CHRISTIAN PAULY
Affiliation:
DPMMS, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB. e-mail: pauly@pmms.cam.ac.uk
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 125 , Issue 2 , January 1999 , pp. 295 - 319
Copyright
Cambridge Philosophical Society 1999

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