### Chain-connected component decomposition of curves on surfaces

Kazuhiro KONNO
Source: J. Math. Soc. Japan Volume 62, Number 2 (2010), 467-486.

#### Abstract

We prove that an arbitrary reducible curve on a smooth surface has an essentially unique decomposition into chain-connected curves. Using this decomposition, we give an upper bound of the geometric genus of a numerically Gorenstein surface singularity in terms of certain topological data determined by the canonical cycle. We show also that the fixed part of the canonical linear system of a 1-connected curve is always rational, that is, the first cohomology of its structure sheaf vanishes.

First Page:
Primary Subjects: 14J29, 14J17
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1273236712
Digital Object Identifier: doi:10.2969/jmsj/06220467
Zentralblatt MATH identifier: 05725851
Mathematical Reviews number (MathSciNet): MR2662852

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