14Mxx Special varieties
This subtopic studies special varieties, including rational, Fano, Calabi–Yau, and other distinguished classes that play central roles in modern geometry.
Specific topics
14M05 Varieties defined by ring conditions
Overview
14M05 studies varieties defined by ring conditions in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Varieties defined by ring conditions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for varieties defined by ring conditions
- 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 special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M06 Linkage in algebraic geometry
Overview
14M06 studies linkage in algebraic geometry in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Linkage in algebraic geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for linkage 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 special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M07 Low codimension problems in algebraic geometry
Overview
14M07 studies low codimension problems in algebraic geometry in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Low codimension problems in algebraic geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for low codimension problems 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 special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M10 Complete intersections
Overview
14M10 studies complete intersections in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Complete intersections (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for complete intersections
- 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 special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M12 Determinantal varieties
Overview
14M12 studies determinantal varieties in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Determinantal varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for determinantal 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
- Study of special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M15 Grassmannians, Schubert varieties, flag manifolds
Overview
14M15 studies grassmannians, schubert varieties, flag manifolds in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Grassmannians, Schubert varieties, flag manifolds (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for grassmannians, schubert varieties, flag manifolds
- 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 special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M17 Homogeneous spaces and generalizations
Overview
14M17 studies homogeneous spaces and generalizations in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Homogeneous spaces and generalizations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for homogeneous spaces and generalizations
- 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 special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M20 Rational and unirational varieties
Overview
14M20 studies rational and unirational varieties in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Rational and unirational varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for rational and unirational 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
- Study of special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M22 Rationally connected varieties
Overview
14M22 studies rationally connected varieties in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Rationally connected varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for rationally connected 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
- Study of special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
Overview
14M25 studies toric varieties, newton polyhedra, okounkov bodies in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Toric varieties, Newton polyhedra, Okounkov bodies (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for toric varieties, newton polyhedra, okounkov bodies
- 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 special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M27 Compactifications; symmetric and spherical varieties
Overview
14M27 studies compactifications; symmetric and spherical varieties in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Compactifications; symmetric and spherical varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for compactifications; symmetric and spherical 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
- Study of special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M30 Supervarieties
Overview
14M30 studies supervarieties in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Supervarieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for supervarieties
- 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 special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks
14M35 Character varieties
Overview
14M35 studies character varieties in special varieties in algebraic geometry. It emphasizes special geometric classes whose defining equations, symmetries, or combinatorial structures make them especially tractable and influential across modern algebraic geometry.
Related Wikipedia Page
Character varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for character 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
- Study of special geometric classes and their invariants
- Connections to representation theory, combinatorics, and moduli
- Applications to mirror symmetry, topology, and mathematical physics
References
Recommended Textbooks