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