学术报告（贾甲 2025.11.11）

摘要：We study the moduli space of higher rank marginally stable pairs (E,s), where E is a torsion free coherent sheaf of rank r on a smooth projective surface and s = (s_1, …, s_r) is a collection of r sections of E. Fixing the Chern character of E, the moduli space is realised as a subscheme of an appropriate Quot–scheme that parametrises quotient sheaves with the corresponding Hilbert polynomial. We establish a precise link between these moduli spaces and the stable minimal models determined by E and its sections, together with the (relative) log canonical model of the base surface. Using the birational geometry of such minimal models, we analyse in detail the components of the Hilbert–Chow morphism from the moduli space to the Hilbert scheme of effective Cartier divisors on the surface. This is a work in progress.