4 problems

Let $(A,H)$ be a principally polarized abelian threefold with Picard rank $\rho(A)=1$. For nonzero $(\beta,n)\in\mathbb{Z}^2$, define…

Donaldson–Thomas multiple-cover formula. Assume $n>0$ or at least two of $d_1,d_2,d_3$ are positive. Then

Multiple-cover formula. For all $g\geq2$, $d_1,d_2>0$, and $d_3\geq0$,

Reduced GW/DT correspondence. The series $Z^{\textup{DT}}_{\beta}(y)$ is the Laurent expansion of a rational function in $y$, and