Voisin map conjecture for homologically trivial zero-cycles

Let $Y$ be the variety in the preceding construction and let $X=F_r(Y)$, with $r\geq 2$, where $\Psi:X\dashrightarrow X$ is the Voisin rational map. For $z\in CH_0(X)_{hom}$, the subgroup of homologically trivial zero-cycles on $X$, Voisin map conjecture.

$$\Psi_*z=(-2)^{r+1}z.$$

This conjecture is presented as a consequence of the conjectural structure of zero-cycles on the varieties $F_r(Y)$; the analogous eigenvalue formula for the holomorphic top form and the degree of $\Psi$ are established in the paper. Its status is not determined by the supplied text.