Plumbing Graphs for Normal Surface-Curve Pairs

Eriko Hironaka

Consider the set of surface-curve pairs (X,C), where X is a normal surface and C is an algebraic curve. In this paper, we define a family F of normal surface-curve pairs, which is closed under coverings, and which contains all smooth surface-curve pairs (X,C), where X is smooth and C has smooth irreducible components with normal crossings. We give a modification of W. Neumann's definition of plumbing graphs, their associated 3-dimensional graph manifolds, and intersection matrices, and use this construction to describe rational intersection matrices and boundary manifolds for regular branched coverings.