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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Subvarieties of $\mathcal{SU}_C(2)$ and $2\theta$-divisors
in the Jacobian


Authors: W. M. Oxbury, C. Pauly and E. Previato
Journal: Trans. Amer. Math. Soc. 350 (1998), 3587-3614
MSC (1991): Primary 14D20, 14H42, 14H60, 14K25
MathSciNet review: 1467474
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Abstract: We explore some of the interplay between Brill-Noether subvarieties of the moduli space ${\mathcal{SU}}_C(2,K)$ of rank 2 bundles with canonical determinant on a smooth projective curve and $2\theta$-divisors, via the inclusion of the moduli space into $|2\Theta|$, singular along the Kummer variety. In particular we show that the moduli space contains all the trisecants of the Kummer and deduce that there are quadrisecant lines only if the curve is hyperelliptic; we show that for generic curves of genus $<6$, though no higher, bundles with $>2$ sections are cut out by $\Gamma _{00}$; and that for genus 4 this locus is precisely the Donagi-Izadi nodal cubic threefold associated to the curve.


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Additional Information

W. M. Oxbury
Affiliation: Department of Mathematical Sciences, Science Laboratories, South Road, Durham DH1 3LE, U.K.
Email: w.m.oxbury@durham.ac.uk

C. Pauly
Affiliation: Laboratoire J. A. Dieudonné, Université de Nice-Sophia-Antipolis, Parc Valrose, F-06108 Nice Cedex 02, France
Email: pauly@math.unice.fr

E. Previato
Affiliation: Department of Mathematics, Boston University, Boston, Massachusetts 02215
Email: ep@math.bu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02148-5
PII: S 0002-9947(98)02148-5
Received by editor(s): September 26, 1996
Article copyright: © Copyright 1998 American Mathematical Society