Manuscripta Mathematica

, Volume 142, Issue 3–4, pp 525–544 | Cite as

On the Hilbert scheme of the moduli space of vector bundles over an algebraic curve

  • L. Brambila-PazEmail author
  • O. Mata-Gutiérrez


Let M(n, ξ) be the moduli space of stable vector bundles of rank n ≥ 3 and fixed determinant ξ over a complex smooth projective algebraic curve X of genus g ≥ 4. We use the gonality of the curve and r-Hecke morphisms to describe a smooth open set of an irreducible component of the Hilbert scheme of M(n, ξ), and to compute its dimension. We prove similar results for the scheme of morphisms \({M or_P (\mathbb{G}, M(n, \xi))}\) and the moduli space of stable bundles over \({X \times \mathbb{G}}\), where \({\mathbb{G}}\) is the Grassmannian \({\mathbb{G}(n - r, \mathbb{C}^n)}\). Moreover, we give sufficient conditions for \({M or_{2ns}(\mathbb{P}^1, M(n, \xi))}\) to be non-empty, when s ≥ 1.

Mathematics Subject Classification (2000)

14H60 14J60 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Centro de Investigación en MatemáticasGuanajuatoMexico

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