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2001 Quadratic vanishing cycles, reduction curves and reduction of the monodromy group of plane curve singularities
Norbert A'Campo
Tohoku Math. J. (2) 53(4): 533-552 (2001). DOI: 10.2748/tmj/1113247799

Abstract

The geometric local monodromy of a plane curve singularity is a diffeomorphism of a compact oriented surface with non empty boundary. The monodromy diffeomorphism is a product of right Dehn twists, where the number of factors is equal to the rank of the first homology of the surface. The core curves of the Dehn twists are quadratic vanishing cycles of the singularity. Moreover, the monodromy diffeomorphism decomposes along reduction curves into pieces, which are invariant, such that the restriction of the monodromy on each piece is isotopic to a diffeomorphism of finite order. In this paper we determine the mutual positions of the core curves of the Dehn twists, which appear in the decomposition of the monodromy, together with the positions of the reduction curves of the monodromy.

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Norbert A'Campo. "Quadratic vanishing cycles, reduction curves and reduction of the monodromy group of plane curve singularities." Tohoku Math. J. (2) 53 (4) 533 - 552, 2001. https://doi.org/10.2748/tmj/1113247799

Information

Published: 2001
First available in Project Euclid: 11 April 2005

zbMATH: 1065.14031
MathSciNet: MR1862217
Digital Object Identifier: 10.2748/tmj/1113247799

Subjects:
Primary: 14H20
Secondary: 14D05, 14H50, 32S40, 32S55

Rights: Copyright © 2001 Tohoku University

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