14Dxx Families and moduli
This subtopic studies families and moduli, focusing on parameter spaces, deformations, and how geometric objects vary in families.
Specific topics
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
Overview
14D05 studies structure of families (picard-lefschetz, monodromy, etc.) in families and moduli in algebraic geometry. It emphasizes variation in families, deformation behavior, and moduli constructions that organize algebraic-geometric objects across parameter spaces.
Related Wikipedia Page
Structure of families (Picard-Lefschetz, monodromy, etc.) (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for structure of families (picard-lefschetz, monodromy, etc.)
- 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
- Study of families and degenerations
- Construction and comparison of moduli spaces
- Links between geometry, arithmetic, and mathematical physics
References
Recommended Textbooks
14D06 Fibrations, degenerations in algebraic geometry
Overview
14D06 studies fibrations, degenerations in algebraic geometry in families and moduli in algebraic geometry. It emphasizes variation in families, deformation behavior, and moduli constructions that organize algebraic-geometric objects across parameter spaces.
Related Wikipedia Page
Fibrations, degenerations in algebraic geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for fibrations, degenerations 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
- Study of families and degenerations
- Construction and comparison of moduli spaces
- Links between geometry, arithmetic, and mathematical physics
References
Recommended Textbooks
14D07 Variation of Hodge structures
Overview
14D07 studies variation of hodge structures in families and moduli in algebraic geometry. It emphasizes variation in families, deformation behavior, and moduli constructions that organize algebraic-geometric objects across parameter spaces.
Related Wikipedia Page
Variation of Hodge structures (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for variation of hodge structures
- 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
- Study of families and degenerations
- Construction and comparison of moduli spaces
- Links between geometry, arithmetic, and mathematical physics
References
Recommended Textbooks
14D10 Arithmetic ground fields (finite, local, global) in algebraic geometry
Overview
14D10 studies arithmetic ground fields (finite, local, global) in algebraic geometry in families and moduli in algebraic geometry. It emphasizes variation in families, deformation behavior, and moduli constructions that organize algebraic-geometric objects across parameter spaces.
Related Wikipedia Page
Arithmetic ground fields (finite, local, global) in algebraic geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for arithmetic ground fields (finite, local, global) 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
- Study of families and degenerations
- Construction and comparison of moduli spaces
- Links between geometry, arithmetic, and mathematical physics
References
Recommended Textbooks
14D15 Formal methods; deformations
Overview
14D15 studies formal methods; deformations in families and moduli in algebraic geometry. It emphasizes variation in families, deformation behavior, and moduli constructions that organize algebraic-geometric objects across parameter spaces.
Related Wikipedia Page
Formal methods; deformations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for formal methods; deformations
- 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
- Study of families and degenerations
- Construction and comparison of moduli spaces
- Links between geometry, arithmetic, and mathematical physics
References
Recommended Textbooks
14D20 Algebraic moduli problems, moduli of vector bundles
Overview
14D20 studies algebraic moduli problems, moduli of vector bundles in families and moduli in algebraic geometry. It emphasizes variation in families, deformation behavior, and moduli constructions that organize algebraic-geometric objects across parameter spaces.
Related Wikipedia Page
Algebraic moduli problems, moduli of vector bundles (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for algebraic moduli problems, moduli of vector bundles
- 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
- Study of families and degenerations
- Construction and comparison of moduli spaces
- Links between geometry, arithmetic, and mathematical physics
References
Recommended Textbooks
14D21 Applications of vector bundles and moduli spaces in mathematical physics
Overview
14D21 studies applications of vector bundles and moduli spaces in mathematical physics in families and moduli in algebraic geometry. It emphasizes variation in families, deformation behavior, and moduli constructions that organize algebraic-geometric objects across parameter spaces.
Related Wikipedia Page
Applications of vector bundles and moduli spaces in mathematical physics (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for applications of vector bundles and moduli spaces in mathematical physics
- 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
- Study of families and degenerations
- Construction and comparison of moduli spaces
- Links between geometry, arithmetic, and mathematical physics
References
Recommended Textbooks
14D22 Fine and coarse moduli spaces
Overview
14D22 studies fine and coarse moduli spaces in families and moduli in algebraic geometry. It emphasizes variation in families, deformation behavior, and moduli constructions that organize algebraic-geometric objects across parameter spaces.
Related Wikipedia Page
Fine and coarse moduli spaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for fine and coarse moduli spaces
- 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
- Study of families and degenerations
- Construction and comparison of moduli spaces
- Links between geometry, arithmetic, and mathematical physics
References
Recommended Textbooks
14D23 Stacks and moduli problems
Overview
14D23 studies stacks and moduli problems in families and moduli in algebraic geometry. It emphasizes variation in families, deformation behavior, and moduli constructions that organize algebraic-geometric objects across parameter spaces.
Related Wikipedia Page
Stacks and moduli problems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for stacks and moduli problems
- 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
- Study of families and degenerations
- Construction and comparison of moduli spaces
- Links between geometry, arithmetic, and mathematical physics
References
Recommended Textbooks
14D24 Geometric Langlands correspondence
Overview
14D24 studies geometric langlands correspondence in families and moduli in algebraic geometry. It emphasizes variation in families, deformation behavior, and moduli constructions that organize algebraic-geometric objects across parameter spaces.
Related Wikipedia Page
Geometric Langlands correspondence (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for geometric langlands correspondence
- 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
- Study of families and degenerations
- Construction and comparison of moduli spaces
- Links between geometry, arithmetic, and mathematical physics
References
Recommended Textbooks