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April, 2010 Chain-connected component decomposition of curves on surfaces
Kazuhiro KONNO
J. Math. Soc. Japan 62(2): 467-486 (April, 2010). DOI: 10.2969/jmsj/06220467

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.

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Kazuhiro KONNO. "Chain-connected component decomposition of curves on surfaces." J. Math. Soc. Japan 62 (2) 467 - 486, April, 2010. https://doi.org/10.2969/jmsj/06220467

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Published: April, 2010
First available in Project Euclid: 7 May 2010

zbMATH: 1193.14047
MathSciNet: MR2662852
Digital Object Identifier: 10.2969/jmsj/06220467

Subjects:
Primary: 14J17 , 14J29

Keywords: reducible curve , singularity

Rights: Copyright © 2010 Mathematical Society of Japan

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Vol.62 • No. 2 • April, 2010
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