Journal of the Mathematical Society of Japan

Chain-connected component decomposition of curves on surfaces

Kazuhiro KONNO

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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

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

Subjects
Primary: 14J29: Surfaces of general type 14J17: Singularities [See also 14B05, 14E15]

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


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