14Nxx Projective and enumerative geometry
This subtopic studies projective and enumerative geometry, where incidence relations and counting problems are studied through geometric methods.
Specific topics
14N05 Projective techniques in algebraic geometry
Overview
14N05 studies projective techniques in algebraic geometry in projective and enumerative geometry. It emphasizes projective constructions and counting problems that turn geometric incidence questions into precise intersection-theoretic and moduli-theoretic statements.
Related Wikipedia Page
Projective techniques in algebraic geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for projective techniques 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
- Enumerative calculations and incidence geometry
- Projective methods for varieties and embeddings
- Connections to quantum cohomology and modern moduli theory
References
Recommended Textbooks
14N10 Enumerative problems in algebraic geometry
Overview
14N10 studies enumerative problems in algebraic geometry in projective and enumerative geometry. It emphasizes projective constructions and counting problems that turn geometric incidence questions into precise intersection-theoretic and moduli-theoretic statements.
Related Wikipedia Page
Enumerative problems in algebraic geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for enumerative 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
- Enumerative calculations and incidence geometry
- Projective methods for varieties and embeddings
- Connections to quantum cohomology and modern moduli theory
References
Recommended Textbooks
14N15 Classical problems, Schubert calculus
Overview
14N15 studies classical problems, schubert calculus in projective and enumerative geometry. It emphasizes projective constructions and counting problems that turn geometric incidence questions into precise intersection-theoretic and moduli-theoretic statements.
Related Wikipedia Page
Classical problems, Schubert calculus (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for classical problems, schubert calculus
- 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
- Enumerative calculations and incidence geometry
- Projective methods for varieties and embeddings
- Connections to quantum cohomology and modern moduli theory
References
Recommended Textbooks
14N20 Configurations of linear subspaces
Overview
14N20 studies configurations of linear subspaces in projective and enumerative geometry. It emphasizes projective constructions and counting problems that turn geometric incidence questions into precise intersection-theoretic and moduli-theoretic statements.
Related Wikipedia Page
Configurations of linear subspaces (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for configurations of linear subspaces
- 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
- Enumerative calculations and incidence geometry
- Projective methods for varieties and embeddings
- Connections to quantum cohomology and modern moduli theory
References
Recommended Textbooks
14N25 Varieties of low degree
Overview
14N25 studies varieties of low degree in projective and enumerative geometry. It emphasizes projective constructions and counting problems that turn geometric incidence questions into precise intersection-theoretic and moduli-theoretic statements.
Related Wikipedia Page
Varieties of low degree (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for varieties of low degree
- 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
- Enumerative calculations and incidence geometry
- Projective methods for varieties and embeddings
- Connections to quantum cohomology and modern moduli theory
References
Recommended Textbooks
14N30 Adjunction problems
Overview
14N30 studies adjunction problems in projective and enumerative geometry. It emphasizes projective constructions and counting problems that turn geometric incidence questions into precise intersection-theoretic and moduli-theoretic statements.
Related Wikipedia Page
Adjunction problems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for adjunction 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
- Enumerative calculations and incidence geometry
- Projective methods for varieties and embeddings
- Connections to quantum cohomology and modern moduli theory
References
Recommended Textbooks
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants
Overview
14N35 studies gromov-witten invariants, quantum cohomology, gopakumar-vafa invariants in projective and enumerative geometry. It emphasizes projective constructions and counting problems that turn geometric incidence questions into precise intersection-theoretic and moduli-theoretic statements.
Related Wikipedia Page
Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for gromov-witten invariants, quantum cohomology, gopakumar-vafa invariants
- 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
- Enumerative calculations and incidence geometry
- Projective methods for varieties and embeddings
- Connections to quantum cohomology and modern moduli theory
References
Recommended Textbooks
14N99 None of the above
Overview
14N99 studies none of the above in projective and enumerative geometry. It emphasizes projective constructions and counting problems that turn geometric incidence questions into precise intersection-theoretic and moduli-theoretic statements.
Related Wikipedia Page
None of the above (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for none of the above
- 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
- Enumerative calculations and incidence geometry
- Projective methods for varieties and embeddings
- Connections to quantum cohomology and modern moduli theory
References
Recommended Textbooks