Divides with cusps and Kirby diagrams for line arrangements

Masahiko Yoshinaga; Sakumi Sugawara

Divides with cusps and Kirby diagrams for line arrangements

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arxiv 2103.15262 v2 pith:FQ3CJUHZ submitted 2021-03-29 math.GT math.CO

Sakumi Sugawara , Masahiko Yoshinaga This is my paper · ORCID

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keywords cuspsdecompositiondescribedividehandlekirbylinespace

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abstract

The complement of a complexified real line arrangement is an affine surface. It is classically known that such a space has a handle decomposition up to $2$-handles. We will describe the handle decomposition induced from Lefschetz hyperplane section theorem for such a space. To describe the Kirby diagram, we introduce the notion of the divide with cusps which is a generalization of the divide introduced by A'Campo.

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Real morsifications via the trace map
math.AG 2026-08 accept novelty 8.0 of 10

Every reduced real plane curve singularity is shown to admit a real morsification, via a new trace map built from nodal smoothings of normalization disks.

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