Diagonal property of the symmetric product of a smooth curve

Let $C$ be an irreducible smooth projective curve defined over an algebraically closed field. We prove that the symmetric product ${\rm Sym}^d©$hasthediagonalpropertyforall$d \geq 1$. For any positive integers $n$ and $r$, let ${\mathcal{Q}}_{{\mathcal{O}}_C^{\oplus n}}(nr)$ be the Quot scheme parametrizing all the torsion quotients of ${\mathcal O}^{\oplus n}C$ofdegree$nr$\mathrm{.}Weprovethat${\mathcal Q}{{\mathcal O}^{\oplus n}_C}(nr)$ has the weak point property.