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