2003/01/02 by Norbert A'Campo, A'Campo, Norbert
Mathematics · #14D05 #14H20 #14H50 #14P25 #57M25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.GT #msc:14D05 #msc:14H20 #msc:14H50 #msc:14P25 #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0301006
16 pages, 6 figures
arxiv created 2003/01/02 · arxiv updated 2009/11/30
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.