Trigonal Morsifications on Hirzebruch Surfaces with an appendix by E. Shustin

2018/10/03 by Andrés Jaramillo Puentes, Puentes, Andrés Jaramillo
Mathematics · #14P25 (Primary) 14H57 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1810.02206

openalex publication_date 2018/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we obtain a classification of rigid isotopy classes of totally reducible trigonal curves lying on a Hirzebruch surface Σ_n, and having a maximal number of non-degenerated double points. Such curves correspond to morsifications of a totally real semiquasihomogeneous singularity of weight (3,3n) (the union of three smooth real branches intersecting each other with multiplicity n). We obtain this classification by studying combinatorial properties of dessins. In the appendix, we prove that any morsification of a totally real semiquasihomogeneous singularity of weight (3,3n) can be realized (up to isotopy) by the restriction of the equation to the Newton diagram and adding monomials under the Newton diagram.

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