Seminar in Real and Complex Geometry
Monday, April 24, 2017, 17:0018:00,
Ornstein building, room 102
Peter Leviant, Tel Aviv University
Morsifications of real plane curve singularities
Abstract
A real morsification of a real plane curve singularity is a real deformation
given by a family of real analytic functions having only real Morse critical
points with all saddles on the zero level. We prove that any real plane curve
singularity admits a real morsification. This was known before only in the case
of all irreducible components of the curve germ being real (A'Campo, Gusein
Zade). We also discuss a relation between real morsifications and the topology
of singularities, extending to arbitrary real morsifications the BalkeKaenders
theorem that states that the A'Campo{GuseinZade diagram associated to
the morsification uniquely determines the topological type of a singularity.
Joint work with E. Shustin.
