Nodal elliptic curves on K3 surfaces

Abstract

The purpose of this note is to study the (total) geometric genus of the compactified Severi curve V L,g−1 consisting of nodal elliptic curves on a general primitively polarized K3 surface (X, L) of genus g.We prove that the genus is bounded below by O(e C √ g ) and conjecture an asymptotic of O(e Cg ).