Statements (67)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical Object
|
| gptkbp:are |
Higher-dimensional Generalizations of Elliptic Curves
|
| gptkbp:associated_with |
gptkb:Jacobian_Varieties
Elliptic Curves Noncommutative Geometry F-theory |
| gptkbp:can_be |
Complex Tori
|
| gptkbp:designatedAs |
Lattice Structures
Polarized Structures |
| gptkbp:dimensions |
2
|
| gptkbp:explores |
Arithmetic Invariants
|
| gptkbp:has |
gptkb:Weil_Conjectures
gptkb:Tate-Shafarevich_Groups gptkb:Fano_Varieties Intersection Theory Rational Maps Riemann-Roch Theorem Riemann Surfaces Cohomological Dimension Moduli Problems Group Structure Symplectic Structures Canonical Divisors Torsion Points Automorphisms Chern_Classes Endomorphism_Rings Hodge_Decomposition Moduli_Spaces_of_Polarized_Varieties Tate's_Theorem |
| https://www.w3.org/2000/01/rdf-schema#label |
Abelian Surfaces
|
| gptkbp:is_a |
gptkb:Abelian_Varieties
gptkb:Kähler_Manifolds Projective Varieties Complex Algebraic Varieties Symplectic Varieties Complex_Manifolds |
| gptkbp:is_essential_for |
Number Theory
|
| gptkbp:is_integrated_with |
Projective Space
|
| gptkbp:is_recognized_for |
Finite Fields
Number Fields Algebraically Closed Fields |
| gptkbp:is_studied_in |
Complex Analysis
Representation Theory Homological Algebra Rational Points Arithmetic Geometry Fibrations Derived Categories Arithmetic Topology Algebraic_Topology Sheaf_Theory |
| gptkbp:is_used_in |
gptkb:Algebraic_Cycles
Cryptography String Theory Geometric Representation Theory Modular Forms Algebraic_Geometry Mathematical_Physics |
| gptkbp:isConnectedTo |
gptkb:Langlands_Program
Mirror Symmetry Galois Representations Tate Modules Moduli_Spaces |
| gptkbp:related_to |
Cohomology Groups
Hodge Structures |
| gptkbp:type |
gptkb:Complex_Algebraic_Variety
|