11 problems

Let $C$ be a smooth curve, and write $g$ for its genus, $\operatorname{gon}(C)$ for its gonality, and $\operatorname{Cliff}(C)$ for its Clifford index. Curves satisfying…

Let $C$ be a smooth curve of genus $g$, let $p$ be a positive integer, and let $L$ be a non-special line bundle of degree … Assume that $L$ is $(p+1)$-very ample, meaning that it s…

Let $C$ be a smooth curve, let ${\cal L}$ be a line bundle on $C$, and let $V\subseteq H^0(C,{\cal L})$ define a linear series. Write $M_{V,{\cal L}}$ for the dual span bundle asso…

Let $C$ be a smooth irreducible projective curve, with gonality $\operatorname{gon} C$ and Clifford index $\operatorname{Cliff} C$. Curves satisfying … are called exceptional curve…

Let $X\to B$ be a general family of genus $g$ stable curves whose general member has Clifford index $\mathfrak{c}$, and let $B$ be a general curve in $\overline{\mathcal D}^r_d$. C…

Higher-rank Mistretta–Stoppino conjecture. The following assertions hold: (i) $E$ is linearly (semi)stable; and (ii) $E$ is linearly (semi)stable if and only if $M_E$ is (semi)stab…

Let $C$ be a curve of genus $g=2n+1$ with maximal Clifford index $\operatorname{Cliff}(C)=n$, and let $L\in\operatorname{Pic}^{2g-2}(C)$ be a non-special line bundle. The Koszul co…

Let $C\subset\mathbb{P}^{g-1}$ be a non-hyperelliptic canonical curve of genus $g\geq 8$ with Clifford index greater than $2$, and let $\mathcal{I}_C$ be its ideal sheaf. Wahl's va…

Barja–González-Alonso–Naranjo conjecture. The inequality

Let $C$ be a smooth curve of Clifford dimension $r\geq 3$, also called an exceptional curve, and let $g$ be its genus. The Clifford dimension is the smallest integer $r$ for which…

Let $C$ be a smooth projective curve, and for each integer $n\geq3$ let $\gamma_n'$ denote the rank-$n$ Clifford index defined using semistable vector bundles, while $\gamma_1$ is…