Abstract
Let X be an irreducible nodal projective hyperelliptic curve of arithmetic genus g. We find explicit descriptions of the moduli spaces of stable vector bundles of rank 2 with a fixed determinant of odd degree on X in terms of spaces associated to the singular pencil of quadrics determined by X.
Similar content being viewed by others
References
Bhosle U.N.: Moduli of orthogonal and spin bundles over hyperelliptic curves. Compositio Mathematica 51, 15–40 (1984)
Bhosle U.N.: Degenerate symplectic and orthogonal bundles on P 1. Math. Ann. 267, 347–364 (1984)
Bhosle U.N.: Pencils of quadrics and hyperelliptic curves in characteristic two. Crelle J. 407, 75–98 (1990)
Bhosle U.N.: Compactified Jacobians of singular hyperelliptic curves. Proc. Indian Acad. Sci. (Math. Sci.) 100(2), 95–102 (1990)
Bhosle U.N.: Generalised parabolic bundles and applications to torsionfree sheaves on nodal curves. Arkiv for Matematik 30(2), 187–215 (1992)
Bhosle, U.N.: Vector bundles of rank two and degree zero on a nodal curve, Proc. Barcelona–Catania Conferences. 1994–1995. Lecture notes in pure and applied Mathematics, vol. 200, pp. 271–281. Marcel-Dekker, New York (1998)
Bhosle U.N.: Moduli of vector bundles in characteristic 2. Math. Nachr. 254/255, 11–26 (2003)
Bhosle U.N.: Maximal subsheaves of torsionfree sheaves on nodal curves. J. Lond. Math. Soc. 2(74), 59–74 (2006)
Bhosle, U.N.: On the moduli of orthogonal bundles on a nodal hyperelliptic curve, Vector Bundles and Complex Geometry: Papers from the Conference in Honor of S. Ramanan on the Occassion of his 70th Birthday (Miraflores de la Sierra, Madrid, 2008), Contemporary Mathematics. American Mathematical Society, Providence (2010)
Desale U.V., Ramanan S.: Classification of vector bundles of rank two on hyperelliptic curves. Invent. Math. 38, 161–185 (1976)
Newstead P.E.: Stable bundles of rank 2 and odd degree over a curve of genus 2. Topology 7, 205–215 (1968)
Narasimhan M.S., Ramanan S.: Moduli of vector bundles on a compact Riemann surface. Ann. Math. 89(1), 19–51 (1969)
Ramanan, S.: Orthogonal and spin bundles over hyperelliptic curves, V.K. Patodi memorial volume. Tata Institute, Bombay (1979)
Author information
Authors and Affiliations
Corresponding author
Additional information
I would like to thank P.E. Newstead for a careful reading of the first version of the paper.
Rights and permissions
About this article
Cite this article
Bhosle, U.N. Moduli of torsionfree sheaves of rank two and odd degree on a nodal hyperelliptic curve. Beitr Algebra Geom 54, 155–179 (2013). https://doi.org/10.1007/s13366-012-0107-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13366-012-0107-5