Diagonal property of the symmetric product of a smooth curve

Abstract

Let C be an irreducible smooth projective curve defined over an algebraically closed field. We prove that the symmetric product Symd(C) has the diagonal property for all d≥1. For any positive integers n and r, let QOC⊕n(nr) be the Quot scheme parameterizing all the torsion quotients of OC⊕n of degree nr. We prove that QOC⊕n(nr) has the weak-point property.