Monodromy of real isolated singularities

Details Monodromy of real isolated singularities Monodromy of real isolated singularities

2003-01-02

arxiv.org/abs/math/0301006v1

Mathematics

Algebraic Geometry

16 pages, 6 figures

Scientific paper

For isolated complex hypersurface singularities with real defining equation we show the existence of a monodromy vector field such that complex conjugation intertwines the local monodromy diffeomorphism with its inverse. In particular, it follows that the geometric monodromy is the composition of the involution induced by complex conjugation and another involution. This topological property holds for all isolated complex plane curve singularities. Using real morsifications, we compute the action of complex conjugation and of the other involution on the Milnor fiber of real plane curve singularities. These involutions have nice descriptions in terms of divides for the singularity.

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