English

Combinatorial study of morsifications of real univariate singularities

Algebraic Geometry 2025-01-15 v2 Combinatorics

Abstract

We study a broad class of morsifications of germs of univariate real analytic functions. We characterize the combinatorial types of the resulting Morse functions, via planar contact trees constructed from Newton-Puiseux roots of the polar curves of the morsifications.

Keywords

Cite

@article{arxiv.2306.04601,
  title  = {Combinatorial study of morsifications of real univariate singularities},
  author = {Arnaud Bodin and Evelia Rosa García Barroso and Patrick Popescu-Pampu and Miruna-Stefana Sorea},
  journal= {arXiv preprint arXiv:2306.04601},
  year   = {2025}
}

Comments

23 pages, 16 figures. Compared to the first version, we clarified some statements as well as Figure 1 and we added Example 6.4 and Remarks 6.8, 7.1. To appear in Mathematische Nachrichten