Severi varieties and branch curves of abelian surfaces of type (1,3)

A polarized abellan surface (A, L) of type (1, 3) induces a 6 : 1 covering of A onto the projective plane with branch curve, a plane curve B of degree 18. The main result of the paper is that for a general abelian surface of type (1, 3), the curve B is irreducible and reduced and admits 72 cusps, 36 nodes or tacnodes, each tacnode counting as 2 nodes, 72 flexes and 36 bitangents. The main idea of the proof is that for a general (A, L) the discriminant curve in the linear system \L\ coincides with the closure of the Severi variety of curves in \L\ admitting a node and is dual to the curve B in the sense of projective geometry.