Nodal elliptic curves on K3 surfaces

Nathan Chen, François Greer, Ruijie Yang

Let $(X,L)$ be a general primitively polarized K3 surface with $c_1(L{)}^2=2g-2$ for some integer $g\ge 2$. The Severi variety $V^{L,\delta }\subset |L|$ is defined to be the locus of…