Affiliation:
1. Mathematisches Institut, Bismarckstr. 1½, D-91054 Erlangen, Germany
2. Dipartimento di Matematica, Università Roma III, L.go S.L. Murialdo 1, 00146 Roma, Italy
Abstract
A polarized abelian 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.
Publisher
World Scientific Pub Co Pte Lt
Cited by
10 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献