6 problems

Maximal-rank conjecture for $h_d$. The element $h_d$ is a maximal rank element on $A$ if and only if either $d=2$, $d=3$ and $n\not\equiv 1\pmod{3}$, or $d=4$ and $n=3$.

Maximal-rank conjecture for $e_d$. The element $e_d$ is a maximal rank element on $A$ if and only if either $d=2$, or $d=3$ and $n\not\equiv 2\pmod{3}$.

Let the restriction maps be those in Theorem, and let $d\geqslant 1$. The paper reports that no counterexamples were found in the tested range $d<d_0(m)$. Maximal Rank Conjecture.…

Maximal-rank conjecture. There exists a constant $K$ such that, for all natural numbers $d,g$ satisfying

Maximal rank conjecture. The multiplication maps $\mu_m$ have maximal rank for all $m$.

Maximal Rank Conjecture. A general embedded smooth curve in $\mathfrak I_{d,g,r}$ has maximal rank: for every integer $n\geq1$, $\nu_n(C)$ is injective or surjective.