2 problems

Coskun–Woolf's stabilization conjecture. Assume $r\geq 1$. Then for each $i\in\mathbb{Z}_{\geq0}$, there is a constant $N(i)$ depending on $i$ such that for every integer $k\leq i$…

Let $(S,H)$ be a polarized surface, let $\beta$ be an effective divisor, and let $M_{\beta,\chi}$ denote the moduli space of polystable one-dimensional sheaves on $S$ with determin…