Lifts of line bundles on curves on K3 surfaces

Kenta Watanabe, Jiryo Komeda

Let $X$ be a K3 surface, let $C$ be a smooth curve of genus $g$ on $X$, and let $A$ be a line bundle of degree $d$ on $C$. Then a line bundle $M$ on $X$ with $M\otimes\mathcal{O}_C…