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Letters in Mathematical Physics

, Volume 108, Issue 6, pp 1551–1561 | Cite as

The very good property for parabolic vector bundles over curves

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Abstract

The purpose of this note is to extend Beilinson and Drinfeld’s “very good” property to moduli stacks of parabolic vector bundles on curves of genuses \(g = 0\) and \(g = 1\). Beilinson and Drinfeld show that for \(g > 1\) a trivial parabolic structure is sufficient for the moduli stacks to be “very good.” We give a sufficient condition on the parabolic structure for this property to hold in the case of nontrivial parabolic structure.

Keywords

Moduli stacks Vector bundles Parabolic bundles Very good property 

Mathematics Subject Classification

14D20 14D23 

References

  1. 1.
    Beilinson, A., Drinfeld, V.: Quantization of Hitchin’s Integrable System and Hecke Eigensheaves. www.math.uchicago.edu/mitya/langlands/hitchin/BD-hitchin.pdf (1991)
  2. 2.
    Crawley-Boevey, W.: On matrices in prescribed conjugacy classes with no common invariant subspace and sum zero. Duke Math. J. 118(2), 339–352 (2003)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Crawley-Boevey, W., Shaw, P.: Multiplicative preprojective algebras, middle convolution and the Deligne–Simpson problem. Adv. Math. 201(1), 180–208 (2006)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Kostov, V.P.: The Deligne–Simpson problem—a survey. J. Algebra 281(1), 83–108 (2004)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Laumon, G.: Un analogue global du cône nilpotent. Duke Math. J. 57(2), 647–671 (1988)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Mehta, V.B., Seshadri, C.S.: Moduli of vector bundles on curves with parabolic structures. Math. Ann. 248(3), 205–239 (1980)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
  8. 8.
    Simpson, C.T.: Products of matrices. In: Differential Geometry, Global Analysis, and Topology (Halifax, NS, 1990), vol. 12 of CMS Conference on Proceedings of American Mathematical Society, pp. 157–185. Providence, RI (1991)Google Scholar
  9. 9.
    Soibelman, A.: Parabolic bundles over the projective line and the Deligne–Simpson problems. Q. J. Math. 67(1), 75–108 (2016)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUSC DornsifeLos AngelesUSA

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