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The Boden-Hu conjecture holds precisely up to rank 8

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Abstract.

We consider moduli schemes of vector bundles over a smooth projective curve endowed with parabolic structures over a marked point. Boden and Hu observed that a slight variation of the weights leads to a desingularisation of the moduli scheme, and they conjectured that one can always obtain a small resolution this way. The present text proves this conjecture in some cases (including all bundles of rank up to eight) and gives counterexamples in all other cases (in particular in every rank beyond eight). The main tool is a generalisation of Ext-groups involving more than two quasiparabolic bundles.

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References

  1. Bhosle, U.N.: Parabolic vector bundles on curves. Ark. Mat. 27 (1), 15–22 (1989)

    MATH  Google Scholar 

  2. Boden, H.U., Hu, Y.: Variations of moduli of parabolic bundles. Math. Ann. 301 (3), 539–559 (1995)

    MATH  Google Scholar 

  3. Goresky, M., MacPherson, R.: Intersection homology. II. Invent. Math. 72 (1), 77–129 (1983)

    MATH  Google Scholar 

  4. Hartshorne, R.: Algebraic geometry. Springer-Verlag, New York, 1977

  5. Hoffmann, N.: On vector bundles over algebraic and arithmetic curves. PhD thesis, University of Bonn, 2002. Bonner Mathematische Schriften 351

  6. Holla, Y.I.: Poincaré polynomial of the moduli spaces of parabolic bundles. Proc. Indian Acad. Sci. Math. Sci. 110 (3), 233–261 (2000)

    MATH  Google Scholar 

  7. Mehta, V.B., Seshadri, C.S.: Moduli of vector bundles on curves with parabolic structures. Math. Ann. 248 (3), 205–239, (1980)

    MATH  Google Scholar 

  8. Seshadri, C.S.: Fibrés vectoriels sur les courbes algébriques, vol. 96 of Astérisque. Société Mathématique de France, Paris, 1982

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  1. Mathematisches Institut der Universität, Bunsenstraße 3–5, 37073, Göttingen, Germany

    N. Hoffmann

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  1. N. Hoffmann
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Correspondence to N. Hoffmann.

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Mathematics Subject Classification (2000): 14H60, 14D20

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Hoffmann, N. The Boden-Hu conjecture holds precisely up to rank 8. Math. Ann. 330, 729–746 (2004). https://doi.org/10.1007/s00208-004-0567-5

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  • DOI: https://doi.org/10.1007/s00208-004-0567-5

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