2 problems

Local Torelli conjecture. The following hold: (a) away from points of $C'$, the fibers of $\alpha$ are smooth or empty; and (b) for a smooth point $p'$ of $C'$, the corresponding p…

For a smooth curve $C$, let $W^r_d(C)$ denote the Brill–Noether locus of line bundles of degree $d$ with at least $r+1$ sections, and let $\operatorname{OC}_3(W^0_d(C),L)$ be the o…