Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 53, Number 4 (2001), 533-552.
Quadratic vanishing cycles, reduction curves and reduction of the monodromy group of plane curve singularities
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.
Tohoku Math. J. (2), Volume 53, Number 4 (2001), 533-552.
First available in Project Euclid: 11 April 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14H20: Singularities, local rings [See also 13Hxx, 14B05]
Secondary: 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.) 14H50: Plane and space curves 32S40: Monodromy; relations with differential equations and D-modules 32S55: Milnor fibration; relations with knot theory [See also 57M25, 57Q45]
A'Campo, Norbert. Quadratic vanishing cycles, reduction curves and reduction of the monodromy group of plane curve singularities. Tohoku Math. J. (2) 53 (2001), no. 4, 533--552. doi:10.2748/tmj/1113247799. https://projecteuclid.org/euclid.tmj/1113247799