14Bxx Local theory
This subtopic studies local theory of algebraic varieties, emphasizing singularity, local structure, and the geometry of neighborhoods of points.
Specific topics
14B05 Singularities
Overview
14B05 studies singularities in local theory in algebraic geometry. It focuses on singular and infinitesimal behavior, deformation phenomena, and local invariants that govern how geometric objects vary in families and neighborhoods.
Related Wikipedia Page
Singularities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for 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 organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Local study of schemes and morphisms
- Deformation and singularity analysis
- Preparation for moduli and intersection-theoretic arguments
References
Recommended Textbooks
14B07 Deformations of singularities
Overview
14B07 studies deformations of singularities in local theory in algebraic geometry. It focuses on singular and infinitesimal behavior, deformation phenomena, and local invariants that govern how geometric objects vary in families and neighborhoods.
Related Wikipedia Page
Deformations of 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 organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Local study of schemes and morphisms
- Deformation and singularity analysis
- Preparation for moduli and intersection-theoretic arguments
References
Recommended Textbooks
14B10 Infinitesimal methods
Overview
14B10 studies infinitesimal methods in local theory in algebraic geometry. It focuses on singular and infinitesimal behavior, deformation phenomena, and local invariants that govern how geometric objects vary in families and neighborhoods.
Related Wikipedia Page
Infinitesimal methods (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for infinitesimal methods
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Local study of schemes and morphisms
- Deformation and singularity analysis
- Preparation for moduli and intersection-theoretic arguments
References
Recommended Textbooks
14B12 Local deformation theory, Artin approximation
Overview
14B12 studies local deformation theory, artin approximation in local theory in algebraic geometry. It focuses on singular and infinitesimal behavior, deformation phenomena, and local invariants that govern how geometric objects vary in families and neighborhoods.
Related Wikipedia Page
Local deformation theory, Artin approximation (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for local deformation theory, artin approximation
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Local study of schemes and morphisms
- Deformation and singularity analysis
- Preparation for moduli and intersection-theoretic arguments
References
Recommended Textbooks
14B15 Local cohomology and algebraic geometry
Overview
14B15 studies local cohomology and algebraic geometry in local theory in algebraic geometry. It focuses on singular and infinitesimal behavior, deformation phenomena, and local invariants that govern how geometric objects vary in families and neighborhoods.
Related Wikipedia Page
Local cohomology and algebraic geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for local cohomology and algebraic geometry
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Local study of schemes and morphisms
- Deformation and singularity analysis
- Preparation for moduli and intersection-theoretic arguments
References
Recommended Textbooks
14B20 Formal neighborhoods in algebraic geometry
Overview
14B20 studies formal neighborhoods in algebraic geometry in local theory in algebraic geometry. It focuses on singular and infinitesimal behavior, deformation phenomena, and local invariants that govern how geometric objects vary in families and neighborhoods.
Related Wikipedia Page
Formal neighborhoods in algebraic geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for formal neighborhoods in algebraic geometry
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Local study of schemes and morphisms
- Deformation and singularity analysis
- Preparation for moduli and intersection-theoretic arguments
References
Recommended Textbooks
14B25 Local structure of morphisms in algebraic geometry
Overview
14B25 studies local structure of morphisms in algebraic geometry in local theory in algebraic geometry. It focuses on singular and infinitesimal behavior, deformation phenomena, and local invariants that govern how geometric objects vary in families and neighborhoods.
Related Wikipedia Page
Local structure of morphisms in algebraic geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for local structure of morphisms in algebraic geometry
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Local study of schemes and morphisms
- Deformation and singularity analysis
- Preparation for moduli and intersection-theoretic arguments
References
Recommended Textbooks