Admin: 1 revision

2014-04-26T09:12:59Z

1 revision

Skr15081997: fixed link.

2014-03-21T13:36:38Z

fixed link.

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{{Navbox
|name = Algebraic curves navbox
|title = Topics in [[algebraic curve]]s
|state = {{{state|autocollapse}}}
|listclass = hlist

|group1 = [[Rational curve]]s
|list1 =
* [[Five points determine a conic]]
* [[Projective line]]
* [[Rational normal curve]]
* [[Riemann sphere]]
* [[Twisted cubic]]

|group2 = [[Elliptic curve]]s
|list2 =
{{Navbox subgroup
|group1 = Analytic theory
|list1 =
* [[Elliptic function]]
* [[Elliptic integral]]
* [[Fundamental pair of periods]]
* [[Modular form]]

|group2 = Arithmetic theory
|list2 =
* [[Counting points on elliptic curves]]
* [[Division polynomial]]s
* [[Hasse's theorem on elliptic curves]]
* [[Mazur's torsion theorem]]
* [[Modular elliptic curve]]
* [[Modularity theorem]]
* [[Mordell–Weil theorem]]
* [[Nagell–Lutz theorem]]
* [[Supersingular elliptic curve]]
* [[Schoof's algorithm]]
* [[Schoof–Elkies–Atkin algorithm]]

|group3 = Applications
|list3 =
* [[Elliptic curve cryptography]]
* [[Elliptic curve primality]]
}}

|group3 = Higher genus
|list3 =
* [[De Franchis theorem]]
* [[Faltings' theorem]]
* [[Hurwitz's automorphisms theorem]]
* [[Hurwitz surface]]
* [[Hyperelliptic curve]]

|group4 = [[Plane curve]]s
|list4 =
* [[AF+BG theorem]]
* [[Bézout's theorem]]
* [[Bitangent]]
* [[Cayley–Bacharach theorem]]
* [[Conic section]]
* [[Cramer's paradox]]
* [[Cubic plane curve]]
* [[Fermat curve]]
* [[Genus–degree formula]]
* [[Hilbert's sixteenth problem]]
* [[Nagata's conjecture on curves]]
* [[Plücker formula]]
* [[Quartic plane curve]]
* [[Real plane curve]]

|group5 = [[Riemann surface]]s
|list5 =
* [[Belyi's theorem]]
* [[Bolza surface]]
* [[Dessin d'enfant]]
* [[Differential of the first kind]]
* [[Klein quartic]]
* [[Riemann's existence theorem]]
* [[Riemann–Roch theorem]]
* [[Teichmüller space]]
* [[Torelli theorem]]

|group6 = Constructions
|list6 =
* [[Dual curve]]
* [[Polar curve]]
* [[Smooth completion]]

|group7 = Structure of curves
|list7 =
{{Navbox subgroup
|group1 = Divisors on curves
|list1 =
* [[Abel–Jacobi map]]
* [[Brill–Noether theory]]
* [[Clifford's theorem on special divisors]]
* [[Gonality of an algebraic curve]]
* [[Jacobian variety]]
* [[Riemann–Roch theorem for algebraic curves]]
* [[Weierstrass point]]
* [[Weil reciprocity law]]

|group2 = Moduli
|list2 =
* [[ELSV formula]]
* [[Gromov–Witten invariant]]
* [[Hodge bundle]]
* [[Moduli of algebraic curves]]
* [[Stable curve]]

|group3 = Morphisms
|list3 =
* [[Hasse–Witt matrix]]
* [[Riemann–Hurwitz formula]]
* [[Prym variety]]
* [[Weber's theorem]]

|group4 = [[Singular point of a curve|Singularities]]
|list4 =
* [[Acnode]]
* [[Crunode]]
* [[Cusp (singularity)|Cusp]]
* [[Delta invariant]]
* [[Tacnode]]

|group5 = [[Vector bundle]]s
|list5 =
* [[Birkhoff–Grothendieck theorem]]
* [[Stable vector bundle]]
* [[Vector bundles on algebraic curves]]
}}
}}<noinclude>
{{collapsible option}}
[[Category:Navigational boxes]]
</noinclude>

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Admin: 1 revision

Skr15081997: fixed link.