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Manuscripta Mathematica

, Volume 136, Issue 1–2, pp 249–271 | Cite as

Torelli theorems for moduli of logarithmic connections and parabolic bundles

  • Ronnie SebastianEmail author
Article
  • 127 Downloads

Abstract

Let Z be a finite subset of a compact connected Riemann Surface X. Let \({\fancyscript{M}_X^{lc}}\) denote the moduli space of pairs (L, D) where L is a line bundle on X and D is a logarithmic connection on L singular along Z. Then \({\fancyscript{M}_X^{lc}}\) has a natural symplectic structure [ω X ]. We show that the pair \({(\fancyscript{M}_X^{lc},[\omega_X])}\) determines X and there are no nonconstant algebraic functions on \({\fancyscript{M}_X^{lc}}\). We also prove a Torelli type theorem for the moduli space of parabolic bundles.

Mathematics Subject Classification (2000)

14C34 14D20 

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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Tata Institute of Fundamental ResearchMumbaiIndia

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