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manuscripta mathematica

, Volume 103, Issue 1, pp 31–46 | Cite as

Poisson structures on moduli spaces¶of parabolic bundles on surfaces

  • Francesco Bottacin
Article

Abstract:

Let X be a smooth complex projective surface and D an effective divisor on X such that H0(X X −1(−D)) ≠ 0. Let us denote by ?ℬ the moduli space of stable parabolic vector bundles on X with parabolic structure over the divisor D (with fixed weights and Hilbert polynomials). We prove that the moduli space ?ℬ is a non-singular quasi-projective variety naturally endowed with a family of holomorphic Poisson structures parametrized by the global sections of ω X −1(−D). This result is the natural generalization to the moduli spaces of parabolic vector bundles of the results obtained in [B2] for the moduli spaces of stable sheaves on a Poisson surface. We also give, in some special cases, a detailed description of the symplectic leaf foliation of the Poisson manifold ?ℬ.

Keywords

Modulus Space Vector Bundle Poisson Structure Global Section Hilbert Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Francesco Bottacin
    • 1
  1. 1.Dipartimento di Ingegneria, Università degli Studi di Bergamo, Viale Marconi 5, 24044 Dalmine (BG), Italy. e-mail: bottacin@math.unipd.itItaly

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