## Journal of the Mathematical Society of Japan

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

Kazuhiro KONNO

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 7 May 2010

https://projecteuclid.org/euclid.jmsj/1273236712

Digital Object Identifier
doi:10.2969/jmsj/06220467

Mathematical Reviews number (MathSciNet)
MR2662852

Zentralblatt MATH identifier
1193.14047

Keywords
reducible curve singularity

#### Citation

KONNO, Kazuhiro. Chain-connected component decomposition of curves on surfaces. J. Math. Soc. Japan 62 (2010), no. 2, 467--486. doi:10.2969/jmsj/06220467. https://projecteuclid.org/euclid.jmsj/1273236712

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