4 problems

Fix positive integers $g,r,d$ with $r\geq 3$ and $\rho(g,r,d)\geq 0$, and let $C$ be a general curve of genus $g$. For a linear series $\ell=(L,V)\in G^r_d(C)$, let…

The Strong Maximal Rank Conjecture. The locus of line bundles $L\in W^r_dC$ for which $\phi^k_L$ is not of maximal rank has dimension

The maximal rank conjecture. The map $\mu_m$ is either injective or surjective.

The strong maximal rank conjecture. For a general $[C]\in\mathcal{M}_g$, the locus $\mathfrak{Quad}_{g,d}^r(C)$ has the expected determinantal dimension