Mathematics Branches, Topics, and Sub-Topics

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32Mxx Complex manifolds

This subtopic studies complex manifolds, emphasizing complex structures, holomorphic coordinates, and the geometry of smooth complex spaces.

Specific topics

32M05 Complex Lie groups, group actions on complex spaces

Overview

32M05 studies complex lie groups, group actions on complex spaces in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.

Related Wikipedia Page

Complex Manifolds (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for complex lie groups, group actions on complex spaces
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in differential geometry, complex analysis, and moduli theory.

Applications

  • Complex differential geometry
  • Holomorphic coordinate atlases
  • Moduli of complex structures

References

Recommended Textbooks

32M10 Homogeneous complex manifolds

Overview

32M10 studies homogeneous complex manifolds in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.

Related Wikipedia Page

Complex Manifolds (Wikipedia)

Useful Links

Key Ideas

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

Typical Uses

Used in differential geometry, complex analysis, and moduli theory.

Applications

  • Complex differential geometry
  • Holomorphic coordinate atlases
  • Moduli of complex structures

References

Recommended Textbooks

32M12 Almost homogeneous manifolds and spaces

Overview

32M12 studies almost homogeneous manifolds and spaces in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.

Related Wikipedia Page

Complex Manifolds (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for almost homogeneous manifolds and spaces
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in differential geometry, complex analysis, and moduli theory.

Applications

  • Complex differential geometry
  • Holomorphic coordinate atlases
  • Moduli of complex structures

References

Recommended Textbooks

32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras

Overview

32M15 studies hermitian symmetric spaces, bounded symmetric domains, jordan algebras in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.

Related Wikipedia Page

Complex Manifolds (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for hermitian symmetric spaces, bounded symmetric domains, jordan algebras
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in differential geometry, complex analysis, and moduli theory.

Applications

  • Complex differential geometry
  • Holomorphic coordinate atlases
  • Moduli of complex structures

References

Recommended Textbooks

32M17 Automorphism groups of $\mathbb{C}^n$ and affine manifolds

Overview

32M17 studies automorphism groups of $\mathbb{c}^n$ and affine manifolds in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.

Related Wikipedia Page

Complex Manifolds (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for automorphism groups of $\mathbb{c}^n$ and affine manifolds
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in differential geometry, complex analysis, and moduli theory.

Applications

  • Complex differential geometry
  • Holomorphic coordinate atlases
  • Moduli of complex structures

References

Recommended Textbooks

32M25 Complex vector fields, holomorphic foliations, related topics

Overview

32M25 studies complex vector fields, holomorphic foliations, related topics in complex manifolds. It studies smooth manifolds with holomorphic coordinate changes and the geometry of complex-analytic structures.

Related Wikipedia Page

Complex Manifolds (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for complex vector fields, holomorphic foliations, related topics
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in differential geometry, complex analysis, and moduli theory.

Applications

  • Complex differential geometry
  • Holomorphic coordinate atlases
  • Moduli of complex structures

References

Recommended Textbooks