On the Hilbert scheme of the moduli space of vector bundles over an algebraic curve |
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Authors: | L. Brambila-Paz O. Mata-Gutiérrez |
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Affiliation: | 1. Centro de Investigación en Matemáticas, Apdo. Postal 402, C.P. 36240, Guanajuato, Gto, Mexico
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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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