14Jxx Surfaces and higher-dimensional varieties
This subtopic studies surfaces and higher-dimensional varieties, emphasizing classification, birational geometry, and the structure of geometric objects in higher dimension.
Specific topics
14J10 Families, moduli, classification: algebraic theory
Overview
14J10 studies families, moduli, classification: algebraic theory in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Families, moduli, classification: algebraic theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for families, moduli, classification: algebraic 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 organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J15 Moduli, classification: analytic theory; relations with modular forms
Overview
14J15 studies moduli, classification: analytic theory; relations with modular forms in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Moduli, classification: analytic theory; relations with modular forms (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for moduli, classification: analytic theory; relations with modular forms
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J17 Singularities of surfaces or higher-dimensional varieties
Overview
14J17 studies singularities of surfaces or higher-dimensional varieties in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Singularities of surfaces or higher-dimensional varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for singularities of surfaces or higher-dimensional 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 organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties
Overview
14J20 studies arithmetic ground fields for surfaces or higher-dimensional varieties in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Arithmetic ground fields for surfaces or higher-dimensional varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for arithmetic ground fields for surfaces or higher-dimensional 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 organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J25 Special surfaces
Overview
14J25 studies special surfaces in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Special surfaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for special surfaces
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J26 Rational and ruled surfaces
Overview
14J26 studies rational and ruled surfaces in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Rational and ruled surfaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for rational and ruled surfaces
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J27 Elliptic surfaces, elliptic or Calabi-Yau fibrations
Overview
14J27 studies elliptic surfaces, elliptic or calabi-yau fibrations in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Elliptic surfaces, elliptic or Calabi-Yau fibrations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for elliptic surfaces, elliptic or calabi-yau fibrations
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J28 $K3$ surfaces and Enriques surfaces
Overview
14J28 studies k3 surfaces and enriques surfaces in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
K3 surfaces and Enriques surfaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for k3 surfaces and enriques surfaces
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J29 Surfaces of general type
Overview
14J29 studies surfaces of general type in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Surfaces of general type (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for surfaces of general type
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J30 $3$-folds
Overview
14J30 studies 3-folds in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
3-folds (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for 3-folds
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J32 Calabi-Yau manifolds and mirror symmetry
Overview
14J32 studies calabi-yau manifolds and mirror symmetry in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Calabi-Yau manifolds and mirror symmetry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for calabi-yau manifolds and mirror symmetry
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J33 Mirror symmetry
Overview
14J33 studies mirror symmetry in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Mirror symmetry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for mirror symmetry
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J35 $4$-folds
Overview
14J35 studies 4-folds in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
4-folds (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for 4-folds
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J40 $n$-folds ($n > 4$)
Overview
14J40 studies n-folds (n > 4) in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
n-folds (n > 4) (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for n-folds (n > 4)
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J45 Fano varieties
Overview
14J45 studies fano varieties in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Fano varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for fano 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 organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J50 Automorphisms of surfaces and higher-dimensional varieties
Overview
14J50 studies automorphisms of surfaces and higher-dimensional varieties in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Automorphisms of surfaces and higher-dimensional varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for automorphisms of surfaces and higher-dimensional 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 organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J60 Vector bundles on surfaces and higher-dimensional varieties
Overview
14J60 studies vector bundles on surfaces and higher-dimensional varieties in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Vector bundles on surfaces and higher-dimensional varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for vector bundles on surfaces and higher-dimensional 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 organize definitions, compare equivalent formulations, and support proof-driven or computational work in algebra and algebraic geometry.
Applications
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J70 Hypersurfaces and algebraic geometry
Overview
14J70 studies hypersurfaces and algebraic geometry in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Hypersurfaces and algebraic geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for hypersurfaces 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J80 Topology of surfaces
Overview
14J80 studies topology of surfaces in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Topology of surfaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for topology of surfaces
- 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks
14J81 Relationships between surfaces and physics
Overview
14J81 studies relationships between surfaces and physics in surfaces and higher-dimensional varieties. It emphasizes classification, moduli, and birational behavior of higher-dimensional varieties, with special focus on surfaces, Calabi-Yau geometry, and geometric structures tied to physics.
Related Wikipedia Page
Relationships between surfaces and physics (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for relationships between surfaces and 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
- Classification of surfaces and higher-dimensional varieties
- Study of special geometries such as K3, Fano, and Calabi-Yau varieties
- Connections to moduli, topology, and mathematical physics
References
Recommended Textbooks