Higher rank Clifford indices of curves on a K3 surface

Soheyla Feyzbakhsh, Chunyi Li

Let $(X,H)$ be a polarized K3 surface with $\mathrm{Pic}(X)=\mathbb{Z}H$, and let $C\in |H|$ be a smooth curve of genus $g$. We give an upper bound on the dimension of global sec…