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Integrable Systems and Torelli Theorems for the Moduli Spaces of Parabolic Bundles and Parabolic Higgs Bundles

  Published:2016-03-04
 Printed: Jun 2016
  • Indranil Biswas,
    School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
  • Tomás L. Gómez,
    Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/ Nicolas Cabrera 15, 28049 Madrid, Spain
  • Marina Logares,
    Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), C/ Nicolas Cabrera 15, 28049 Madrid, Spain
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Abstract

We prove a Torelli theorem for the moduli space of semistable parabolic Higgs bundles over a smooth complex projective algebraic curve under the assumption that the parabolic weight system is generic. When the genus is at least two, using this result we also prove a Torelli theorem for the moduli space of semistable parabolic bundles of rank at least two with generic parabolic weights. The key input in the proofs is a method of J.C. Hurtubise.
Keywords: parabolic bundle, Higgs field, Torelli theorem parabolic bundle, Higgs field, Torelli theorem
MSC Classifications: 14D22, 14D20 show english descriptions Fine and coarse moduli spaces
Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
14D22 - Fine and coarse moduli spaces
14D20 - Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
 

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