7 problems

Let $X$ be the variety under consideration, let $D\in \operatorname{Div}(X)\otimes \mathbb{Q}$ be a divisor class on the boundary of the effective cone, and let $\eta\in X$ be a ge…

Let $G$ be a finite, undirected, connected, loop-free multigraph of genus $g$. Define the Brill-Noether number by … A divisor on $G$ has a degree and a rank in the usual graph-theo…

Gonality-tight graph conjecture. The following hold:

Threefold numerical-effectivity conjecture. Then $L$ is numerically equivalent to an effective divisor.

Let $\Gamma$ be a smooth tropicalization of an algebraic curve $C$. An internal divisor is a divisor lying in a cell $\sigma$ of $|\mathcal{D}_{\Gamma}|$ parametrizing divisors wit…

For an effective divisor $D=a\lambda-b\delta$ on $\overline{\mathcal M}_g$ with $a,b>0$, define its slope by … Here $g$ tends to infinity. Asymptotic sharp-slope conjecture. There…

Let $\Gamma$ be a metric graph of genus $g$. A minimal rank-determining set is a rank-determining set of $\Gamma$ that has no proper subset that is rank-determining. Cardinality bo…