Advanced Studies in Pure Mathematics

Plumbing Graphs for Normal Surface-Curve Pairs

Eriko Hironaka

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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

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

First available in Project Euclid: 20 August 2018

Permanent link to this document euclid.aspm/1534788968

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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.

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