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

摘要

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.