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Zero-Dimensional Schemes for Singularities

  • Gert-Martin GreuelEmail author
  • Christoph Lossen
  • Eugenii Shustin
Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

This section is devoted to the study of zero-dimensional schemes in a smooth projective surface \(\varSigma \), associated to and concentrated in the (finite) set of singular points of a reduced curve C on \(\varSigma \). In this chapter, a curve (singularity) we will always mean a reduced curve (singularity), unless we explicitly say the opposite. We introduce the notion of cluster schemes (cf. Sect. 1.1.2) which allows us to encode the topological type of the singularities of C and, in Sect. 1.1.4, a class of zero-dimensional schemes encoding the analytic type of the singularities.

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Copyright information

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Authors and Affiliations

  • Gert-Martin Greuel
    • 1
    Email author
  • Christoph Lossen
    • 1
  • Eugenii Shustin
    • 2
  1. 1.Fachbereich MathematikTU KaiserslauternKaiserslauternGermany
  2. 2.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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