32Cxx Analytic spaces
This subtopic studies analytic spaces, including local and global analytic structures that generalize complex manifolds and varieties.
Specific topics
32C05 Real-analytic manifolds, real-analytic spaces
Overview
32C05 studies real-analytic manifolds, real-analytic spaces in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for real-analytic manifolds, real-analytic 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 local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C07 Real-analytic sets, complex Nash functions
Overview
32C07 studies real-analytic sets, complex nash functions in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for real-analytic sets, complex nash functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C09 Embedding of real analytic manifolds
Overview
32C09 studies embedding of real analytic manifolds in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for embedding of real analytic 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 local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C11 Complex supergeometry
Overview
32C11 studies complex supergeometry in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for complex supergeometry
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C15 Complex spaces
Overview
32C15 studies complex spaces in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for 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 local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C18 Topology of analytic spaces and holomorphic mappings
Overview
32C18 studies topology of analytic spaces and holomorphic mappings in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for topology of analytic spaces and holomorphic mappings
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C20 Normal analytic spaces
Overview
32C20 studies normal analytic spaces in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for normal analytic 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 local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C22 Embedding of analytic spaces
Overview
32C22 studies embedding of analytic spaces in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for embedding of analytic 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 local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C25 Analytic subsets and submanifolds
Overview
32C25 studies analytic subsets and submanifolds in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for analytic subsets and submanifolds
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C30 Integration on analytic sets and spaces, currents
Overview
32C30 studies integration on analytic sets and spaces, currents in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for integration on analytic sets and spaces, currents
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C35 Analytic sheaves and cohomology groups
Overview
32C35 studies analytic sheaves and cohomology groups in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for analytic sheaves and cohomology groups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C36 Local cohomology of analytic spaces
Overview
32C36 studies local cohomology of analytic spaces in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for local cohomology of analytic 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 local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C37 Duality theorems for analytic spaces
Overview
32C37 studies duality theorems for analytic spaces in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for duality theorems for analytic 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 local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C38 Sheaves of differential operators and their modules, $D$-modules
Overview
32C38 studies sheaves of differential operators and their modules, $d$-modules in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for sheaves of differential operators and their modules, $d$-modules
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks
32C55 The Levi problem in complex spaces; generalizations
Overview
32C55 studies the levi problem in complex spaces; generalizations in analytic spaces. It studies complex spaces defined by local analytic data and the sheaf-theoretic structures that describe them.
Related Wikipedia Page
Analytic Spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for the levi problem in complex spaces; generalizations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in local complex geometry, sheaf theory, and singularity analysis.
Applications
- Complex spaces and germs
- Sheaf-theoretic methods
- Local singularity structure
References
Recommended Textbooks