Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

32Bxx Local analytic geometry

This subtopic studies local analytic geometry, focusing on germs, local rings, and the structure of complex-analytic singularities.

Specific topics

32B05 Analytic algebras and generalizations, preparation theorems

Overview

32B05 studies analytic algebras and generalizations, preparation theorems in local analytic geometry. It studies analytic sets and local geometric structure in complex spaces, emphasizing germs, singularities, and local models.

Related Wikipedia Page

Local Analytic Geometry (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for analytic algebras and generalizations, preparation theorems
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to understand local behavior of complex analytic varieties.

Applications

  • Germs and local models
  • Singularity analysis
  • Coherent analytic geometry

References

Recommended Textbooks

32B10 Germs of analytic sets, local parametrization

Overview

32B10 studies germs of analytic sets, local parametrization in local analytic geometry. It studies analytic sets and local geometric structure in complex spaces, emphasizing germs, singularities, and local models.

Related Wikipedia Page

Local Analytic Geometry (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for germs of analytic sets, local parametrization
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to understand local behavior of complex analytic varieties.

Applications

  • Germs and local models
  • Singularity analysis
  • Coherent analytic geometry

References

Recommended Textbooks

32B15 Analytic sets, complex analytic sets

Overview

32B15 studies analytic sets, complex analytic sets in local analytic geometry. It studies analytic sets and local geometric structure in complex spaces, emphasizing germs, singularities, and local models.

Related Wikipedia Page

Local Analytic Geometry (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for analytic sets, complex analytic sets
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to understand local behavior of complex analytic varieties.

Applications

  • Germs and local models
  • Singularity analysis
  • Coherent analytic geometry

References

Recommended Textbooks

32B20 Semi-analytic sets and subanalytic sets

Overview

32B20 studies semi-analytic sets and subanalytic sets in local analytic geometry. It studies analytic sets and local geometric structure in complex spaces, emphasizing germs, singularities, and local models.

Related Wikipedia Page

Local Analytic Geometry (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for semi-analytic sets and subanalytic sets
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to understand local behavior of complex analytic varieties.

Applications

  • Germs and local models
  • Singularity analysis
  • Coherent analytic geometry

References

Recommended Textbooks

32B25 Triangulation and related questions

Overview

32B25 studies triangulation and related questions in local analytic geometry. It studies analytic sets and local geometric structure in complex spaces, emphasizing germs, singularities, and local models.

Related Wikipedia Page

Local Analytic Geometry (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for triangulation and related questions
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to understand local behavior of complex analytic varieties.

Applications

  • Germs and local models
  • Singularity analysis
  • Coherent analytic geometry

References

Recommended Textbooks