Statements (94)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:canBe |
Affine
Nonsingular Projective Singular |
| gptkbp:class |
gptkb:genus
Degree Singularities |
| gptkbp:definedIn |
Zero set of a polynomial in two variables
|
| gptkbp:dimensions |
One
|
| gptkbp:example |
Elliptic curve
Hyperelliptic curve Conic section Plane cubic curve |
| gptkbp:field |
gptkb:Algebraic_geometry
|
| gptkbp:hasApplication |
gptkb:Algebraic_coding_theory
gptkb:Cryptosystems Mathematical physics Coding theory |
| gptkbp:hasInvariant |
gptkb:genus
gptkb:Arithmetic_genus gptkb:Geometric_genus Degree |
| gptkbp:hasProperty |
Can be birationally equivalent
Can be classified by Jacobian Can be classified by Picard group Can be classified by Weierstrass points Can be classified by affine models Can be classified by automorphism group Can be classified by automorphisms Can be classified by branch points Can be classified by covering maps Can be classified by degree Can be classified by desingularization Can be classified by divisor class group Can be classified by embeddings Can be classified by field extensions Can be classified by field of definition Can be classified by function field Can be classified by genus Can be classified by gonality Can be classified by moduli space Can be classified by morphisms Can be classified by normalization Can be classified by projective models Can be classified by ramification Can be classified by resolution of singularities Can be classified by singularities Can be compact Can be complete Can be defined by homogeneous polynomials Can be defined by inhomogeneous polynomials Can be defined over algebraically closed fields Can be defined over any field Can be defined over arbitrary fields Can be defined over complex numbers Can be defined over finite fields Can be defined over function fields Can be defined over number fields Can be defined over p-adic fields Can be defined over rational numbers Can be defined over real numbers Can be diffeomorphic Can be elliptic Can be embedded in affine space Can be embedded in projective space Can be homeomorphic Can be hyperelliptic Can be incomplete Can be irreducible Can be isomorphic Can be open Can be parametrized Can be plane or space curves Can be rational Can be reducible Can be reducible or irreducible Can be singular Can be smooth Can have singular points |
| https://www.w3.org/2000/01/rdf-schema#label |
Algebraic Curves
|
| gptkbp:importantFor |
gptkb:Number_theory
gptkb:Topology Cryptography Complex analysis |
| gptkbp:relatedTo |
gptkb:Riemann_surfaces
Function fields |
| gptkbp:studiedBy |
Algebraic geometers
|
| gptkbp:studiedIn |
gptkb:Mathematics
gptkb:Intersection_theory gptkb:Sheaf_theory gptkb:Divisor_theory |
| gptkbp:bfsParent |
gptkb:William_Fulton
|
| gptkbp:bfsLayer |
6
|