14Txx Tropical geometry
This subtopic studies tropical geometry, where combinatorial shadow methods are used to study algebraic geometry through piecewise-linear structures.
Specific topics
14T05 Tropical geometry
Overview
14T05 studies tropical geometry in tropical geometry. It develops piecewise-linear shadows of algebraic geometry, with emphasis on valuations, combinatorics, and degeneration phenomena.
Related Wikipedia Page
Tropical geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for tropical 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
- Combinatorial models of algebraic varieties
- Degeneration techniques and valuations
- Applications to enumerative geometry and mirror symmetry
References
Recommended Textbooks
14T10 Foundations of tropical geometry
Overview
14T10 studies foundations of tropical geometry in tropical geometry. It develops piecewise-linear shadows of algebraic geometry, with emphasis on valuations, combinatorics, and degeneration phenomena.
Related Wikipedia Page
Foundations of tropical geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for foundations of tropical 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
- Combinatorial models of algebraic varieties
- Degeneration techniques and valuations
- Applications to enumerative geometry and mirror symmetry
References
Recommended Textbooks
14T15 Combinatorial aspects of tropical varieties
Overview
14T15 studies combinatorial aspects of tropical varieties in tropical geometry. It develops piecewise-linear shadows of algebraic geometry, with emphasis on valuations, combinatorics, and degeneration phenomena.
Related Wikipedia Page
Combinatorial aspects of tropical varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for combinatorial aspects of tropical 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
- Combinatorial models of algebraic varieties
- Degeneration techniques and valuations
- Applications to enumerative geometry and mirror symmetry
References
Recommended Textbooks
14T20 Geometric aspects of tropical varieties
Overview
14T20 studies geometric aspects of tropical varieties in tropical geometry. It develops piecewise-linear shadows of algebraic geometry, with emphasis on valuations, combinatorics, and degeneration phenomena.
Related Wikipedia Page
Geometric aspects of tropical varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for geometric aspects of tropical 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
- Combinatorial models of algebraic varieties
- Degeneration techniques and valuations
- Applications to enumerative geometry and mirror symmetry
References
Recommended Textbooks
14T25 Arithmetic aspects of tropical varieties
Overview
14T25 studies arithmetic aspects of tropical varieties in tropical geometry. It develops piecewise-linear shadows of algebraic geometry, with emphasis on valuations, combinatorics, and degeneration phenomena.
Related Wikipedia Page
Arithmetic aspects of tropical varieties (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for arithmetic aspects of tropical 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
- Combinatorial models of algebraic varieties
- Degeneration techniques and valuations
- Applications to enumerative geometry and mirror symmetry
References
Recommended Textbooks
14T90 Applications of tropical geometry
Overview
14T90 studies applications of tropical geometry in tropical geometry. It develops piecewise-linear shadows of algebraic geometry, with emphasis on valuations, combinatorics, and degeneration phenomena.
Related Wikipedia Page
Applications of tropical geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for applications of tropical 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
- Combinatorial models of algebraic varieties
- Degeneration techniques and valuations
- Applications to enumerative geometry and mirror symmetry
References
Recommended Textbooks
14T99 None of the above
Overview
14T99 studies none of the above in tropical geometry. It develops piecewise-linear shadows of algebraic geometry, with emphasis on valuations, combinatorics, and degeneration phenomena.
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
- Combinatorial models of algebraic varieties
- Degeneration techniques and valuations
- Applications to enumerative geometry and mirror symmetry
References
Recommended Textbooks