3 problems

Global generation conjecture. For any $r\geq 1$, $\mathcal{O}_{U}(k\Theta_N)$ is globally generated on $U_X(r,0)$ for $k\geq r+1$.

Rigid special presentation conjecture. There exists an irreducible, regular component $\mathcal B\subseteq\widetilde{B_C^{k_i}}(d)$ such that

Let $X$ be a smooth projective curve, and let $SU_X(r,d)$ denote the moduli space of semistable vector bundles of rank $r$ and degree $d$, with generalized theta line bundle…