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A Torelli type theorem for the moduli space of parabolic vector bundles over curves

Published online by Cambridge University Press:  26 March 2001

V. BALAJI ,
INDRANIL BISWAS  and
SEBASTIAN DEL BAÑO ROLLIN
V. BALAJI
Affiliation:
School of Mathematics, SPIC Mathematical Institute, 92 G.N. Chetty Road, T. Nagar, Madras 600017, India; e-mail: balaji@smi.ernet.in
INDRANIL BISWAS
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India; e-mail: indranil@math.tifr.res.in
SEBASTIAN DEL BAÑO ROLLIN
Affiliation:
Max Planck Institut für Mathematik, Gottfried-Claren-Strasse 26, D-53225 Bonn, Germany; e-mail: sebas@mpim-bonn.mpg.de
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Abstract

Let S (respectively, S′) be a finite subset of a compact connected Riemann surface X (respectively, X′) of genus at least two. Let [Mscr ] (respectively, [Mscr ]′) denote a moduli space of parabolic stable bundles of rank 2 over X (respectively, X′) with fixed determinant of degree 1, having a nontrivial quasi-parabolic structure over each point of S (respectively, S′) and of parabolic degree less than 2. It is proved that [Mscr ] is isomorphic to [Mscr ]′ if and only if there is an isomorphism of X with X′ taking S to S′.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 2 , March 2001 , pp. 269 - 280
Copyright
2001 Cambridge Philosophical Society

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