12 problems

Noether's maximal rank conjecture. The map $\rho_m$ should have maximal rank for sufficiently general embeddings of sufficiently general curves.

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 $n\not\equiv 2\pmod{3}$.

Classical maximal rank conjecture. The map should always be injective or surjective, and the analogous assertion should hold for the higher-order multiplication maps.

Let $C$ be a general curve of genus $g$, and let $W^r_d(C)$ be the variety of linear systems of degree $d$ and dimension at least $r$. For positive integers $r,d$ satisfying … wher…

Eisenbud–Harris maximal rank conjecture. The map $\phi_L$ has maximal rank.

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 map $\mu_k$ has maximal rank, meaning that it is either injective or surjective.

Quadratic maximal rank prediction. The maximal rank conjecture predicts that $\mu_2$ is injective for a general linear series on a general curve exactly when $r\leq 2s$.

Tropical maximal rank conjecture. Suppose $r\geq 3$, $\rho(g,r,d)\geq 0$, and $d<g+r$. Then there is a divisor $D$ of rank $r$ and degree $d$ whose class is vertex avoiding on a ch…

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