Abstract
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.
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Brambila-Paz, L., Mata-Gutiérrez, O. On the Hilbert scheme of the moduli space of vector bundles over an algebraic curve. manuscripta math. 142, 525–544 (2013). https://doi.org/10.1007/s00229-013-0618-x
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DOI: https://doi.org/10.1007/s00229-013-0618-x