TY - JOUR

T1 - Morsifications of real plane curve singularities

AU - Leviant, Peter

AU - Shustin, Eugenii

N1 - Publisher Copyright:
© 2018, Worldwide Center of Mathematics. All rights reserved.

PY - 2018

Y1 - 2018

N2 - 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 the existence of real morsifications for real plane curve singularities having arbitrary real local branches and pairs of complex conjugate branches satisfying some conditions. This was known before only in the case of all local branches 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, which states that the A’Campo–Gusein-Zade diagram associated to a morsification uniquely determines the topological type of a singularity.

AB - 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 the existence of real morsifications for real plane curve singularities having arbitrary real local branches and pairs of complex conjugate branches satisfying some conditions. This was known before only in the case of all local branches 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, which states that the A’Campo–Gusein-Zade diagram associated to a morsification uniquely determines the topological type of a singularity.

UR - http://www.scopus.com/inward/record.url?scp=85057100971&partnerID=8YFLogxK

U2 - 10.5427/jsing.2018.18p

DO - 10.5427/jsing.2018.18p

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AN - SCOPUS:85057100971

SN - 1949-2006

VL - 18

SP - 307

EP - 328

JO - Journal of Singularities

JF - Journal of Singularities

ER -