4 problems

Let $\bar{G}=(G,\omega)$ be a vertex-weighted graph, and let $\delta$ be a divisor class on $G$. The algebraic rank $r_{\bar{G}}^{\operatorname{alg}}(\delta)$ is defined using noda…

Caporaso's algebro-geometric rank conjecture. One has

The algebraic interpretation conjecture. For every graph $G$ and divisor class $\delta\in\operatorname{Pic}(G)$,

Let $\Gamma$ be a metric graph of genus $g$. A subset of points on $\Gamma$ is rank determining if checking the rank of a divisor after subtracting effective divisors supported on…