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Superisolated Singularities and Friends

In: Handbook of Geometry and Topology of Singularities VIII

Author

Listed:
  • Enrique Artal Bartolo

    (Departamento de Matemáticas, IUMA, Universidad de Zaragoza)

Abstract

Superisolated surface singularities in ( ℂ 3 , 0 ) $$(\mathbb {C}^3,0)$$ were introduced by I. Luengo to prove that the μ $$\mu $$ -constant stratum may be singular. The main feature of this family is that it can bring information from the projective plane curves (global setting but smaller dimension) into surface singularities. They are simple enough to allow to retrieve information and complicated enough to offer a variety of properties. The so-called Lê-Yomdin singularities are a generalization which offers a wider catalog of examples. We study some properties of these singularities, mainly topological and related with the monodromy, and we introduce another family which exploits the same properties but in the quasi-homogeneous setting.

Suggested Citation

  • Enrique Artal Bartolo, 2026. "Superisolated Singularities and Friends," Springer Books, in: José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities VIII, chapter 0, pages 145-188, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-99571-2_4
    DOI: 10.1007/978-3-031-99571-2_4
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