2 problems

Bounded strong Donagi–Morrison conjecture. There is a bound $\beta$ depending on $C$ and $S$ such that, if $d<\beta$, then there is a line bundle $N\hookrightarrow E_{C,A}$ with…

Strong Donagi–Morrison conjecture. There is a nontrivial line bundle $N\hookrightarrow E_{C,A}$ with $h^0(S,N)\geq 2$ such that $E_{C,A}/N$ is stable.