## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Arrangements – Tokyo 1998, M. Falk and H. Terao, eds. (Tokyo: Mathematical Society of Japan, 2000), 127 - 144

### Plumbing Graphs for Normal Surface-Curve Pairs

#### Abstract

Consider the set of surface-curve pairs $(X,\mathcal{C})$, where $X$ is a normal surface and $\mathcal{C}$ is an algebraic curve. In this paper, we define a family $\mathcal{F}$ of *normal* surface-curve pairs, which is closed under coverings, and which contains all *smooth* surface-curve pairs $(X, \mathcal{C})$, where $X$ is smooth and $\mathcal{C}$ 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.

#### Article information

**Source***Arrangements – Tokyo 1998*, M. Falk and H. Terao, eds. (Tokyo: Mathematical Society of Japan, 2000), 127-144

**Dates**

First available in Project Euclid:
20 August 2018

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1534788968

**Digital Object Identifier**

doi:10.2969/aspm/02710127

**Mathematical Reviews number (MathSciNet)**

MR1796896

**Zentralblatt MATH identifier**

1016.57016

#### Citation

Hironaka, Eriko. Plumbing Graphs for Normal Surface-Curve Pairs. Arrangements – Tokyo 1998, 127--144, Mathematical Society of Japan, Tokyo, Japan, 2000. doi:10.2969/aspm/02710127. https://projecteuclid.org/euclid.aspm/1534788968