Conjecture on the intersection Betti numbers of moduli spaces of sheaves on the plane

Let $M_{(0,d,\chi)}$ be the moduli space of Gieseker semistable sheaves on $\mathbb P^2$ with Chern character $(0,d,\chi)$, and write its intersection Betti numbers as $Ib_j(M_{d,\chi})$. For fixed $d\geq 1$, the values of $\chi$ index moduli spaces that need not be isomorphic, although tensoring by $\mathcal O(1)$ and Serre duality identify some of them. Intersection-Betti-number conjecture. For every fixed $d\geq 1$, the intersection Betti numbers $Ib_j(M_{d,\chi})$ do not depend on $\chi$. This predicts an invariant of the moduli spaces that is finer than their isomorphism type; the source gives no resolution of the conjecture.