Seminar in Real and Complex Geometry

Monday, April 24, 2017, 17:00-18:00, Ornstein building, room 102

Peter Leviant, Tel Aviv University

Morsifications of real plane curve singularities


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 Balke-Kaenders theorem that states that the A'Campo{Gusein-Zade diagram associated to the morsification uniquely determines the topological type of a singularity. Joint work with E. Shustin.