32Sxx Singularities
This subtopic studies singularities, focusing on local structure, resolution, and analytic classification of non-regular points.
Specific topics
32S05 Local complex singularities
Overview
32S05 studies local complex singularities in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for local complex singularities
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S10 Invariants of analytic local rings
Overview
32S10 studies invariants of analytic local rings in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for invariants of analytic local rings
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S15 Equisingularity (topological and analytic)
Overview
32S15 studies equisingularity (topological and analytic) in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for equisingularity (topological and analytic)
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S20 Global theory of singularities
Overview
32S20 studies global theory of singularities in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for global theory of singularities
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S22 Relations with arrangement of hyperplanes
Overview
32S22 studies relations with arrangement of hyperplanes in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for relations with arrangement of hyperplanes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S25 Surface and hypersurface singularities
Overview
32S25 studies surface and hypersurface singularities in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for surface and hypersurface singularities
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S30 Deformations of singularities
Overview
32S30 studies deformations of singularities in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for deformations of singularities
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S35 Mixed Hodge theory of singular varieties
Overview
32S35 studies mixed hodge theory of singular varieties in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for mixed hodge theory of singular varieties
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S40 Monodromy; relations with differential equations and $D$-modules
Overview
32S40 studies monodromy; relations with differential equations and $d$-modules in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for monodromy; relations with differential equations and $d$-modules
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S45 Modifications
Overview
32S45 studies modifications in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for modifications
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S50 Topological aspects: Lefschetz theorems, topological classification
Overview
32S50 studies topological aspects: lefschetz theorems, topological classification in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for topological aspects: lefschetz theorems, topological classification
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S55 Milnor fibration; relations with knot theory
Overview
32S55 studies milnor fibration; relations with knot theory in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for milnor fibration; relations with knot theory
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S60 Stratifications; constructible sheaves; intersection cohomology
Overview
32S60 studies stratifications; constructible sheaves; intersection cohomology in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for stratifications; constructible sheaves; intersection cohomology
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S65 Singularities of holomorphic vector fields and foliations
Overview
32S65 studies singularities of holomorphic vector fields and foliations in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for singularities of holomorphic vector fields and foliations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks
32S70 Other operations on analytic singularities
Overview
32S70 studies other operations on analytic singularities in singularities. It studies analytic and geometric singularities, including local invariants, resolution, and deformation behavior.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other operations on analytic singularities
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to classify and resolve singular points in complex geometry.
Applications
- Resolution of singularities
- Local invariants and deformations
- Singularity classification
References
Recommended Textbooks