Johnson's Quot-scheme integral conjecture

Let $X$ be a smooth projective surface with $\chi(\mathcal{O}_X)=1$, let $f$ be the invariants of an ideal sheaf of $k$ points, let $V$ be a vector bundle such that $\operatorname{Quot}(V,k)$ has expected dimension zero, and let $e^*$ denote the invariants of the kernels of the parametrized surjections. Johnson's Quot-scheme integral conjecture.

$$\int_{X^{[k]}} c_{2k}({V^*}^{[k]})=\chi(X^{[k]},\mathcal{O}_{X^{[k]}}(\Theta_e)).$$

The expected dimension is zero exactly when $\chi(e\cdot f)=0$. The conjecture relates a top Chern-class integral counting finite Quot schemes to the Euler characteristic of a determinant line bundle; the source does not state a general proof.