List of algebraic geometry topics
From Wikipedia, the free encyclopedia
This is a list of algebraic geometry topics, by Wikipedia page.
Contents |
[edit] Classical topics in projective geometry
- Affine space
- Projective space
- Projective line, cross-ratio
- Projective plane
- Complex projective space
- Plane at infinity, hyperplane at infinity
- Projective frame
- Projective transformation
- Fundamental theorem of projective geometry
- Duality (projective geometry)
- Real projective plane
- Real projective space
- Segre embedding, multi-way projective space
- Rational normal curve
[edit] Algebraic curves
- Conics, Pascal's theorem, Brianchon's theorem
- Twisted cubic
- Elliptic curve, cubic curve
- Hyperelliptic curve
- Klein quartic
- modular curve
- Fermat curve
- Bézout's theorem
- Brill-Noether theory
- Genus (mathematics)
- Riemann surface
- Riemann-Hurwitz formula
- Riemann-Roch theorem
- Abelian integral
- Differential of the first kind
- Jacobian variety
- Hurwitz's automorphisms theorem
- Clifford's theorem
- Gonality of an algebraic curve
- Weil's reciprocity law
- Goppa code
[edit] Algebraic surfaces
- Enriques-Kodaira classification
- List of algebraic surfaces
- Ruled surface
- Cubic surface
- Veronese surface
- Del Pezzo surface
- Rational surface
- Enriques surface
- K3 surface
- Hodge index theorem
- Elliptic surface
- Surface of general type
- Zariski surface
[edit] Algebraic geometry: classical approach
- Algebraic variety
- Tangent space, Zariski tangent space
- Function field
- Ample vector bundle
- Linear system of divisors
- Birational geometry
- Intersection number
- Albanese variety
- Picard group
- Pluricanonical ring
- Modular form
- Moduli space
- Modular equation
- Algebraic function
- Algebraic form
- Addition theorem
- Invariant theory
- Geometric invariant theory
- Toric geometry
- Deformation theory
- Singular point, non-singular
- Singularity theory
- Weil conjectures
[edit] Complex manifolds
- Kähler manifold
- Calabi-Yau manifold
- Stein manifold
- Hodge theory
- Hodge cycle
- Hodge conjecture
- Algebraic geometry and analytic geometry
- Mirror symmetry
[edit] Algebraic groups
- Identity component
- Linear algebraic group
- Abelian variety
- Grassmannian
- Flag manifold
- Algebraic torus
- Weil restriction
- Differential Galois theory
[edit] Contemporary foundations
Main article glossary of scheme theory
[edit] Commutative algebra
- Prime ideal
- Valuation (mathematics)
- Regular local ring
- Regular sequence (algebra)
- Cohen-Macaulay ring
- Gorenstein ring
- Koszul complex
- Spectrum of a ring
- Zariski topology
- Kähler differential
[edit] Sheaf theory
- Locally ringed space
- Coherent sheaf
- Invertible sheaf
- Sheaf cohomology
- Hirzebruch-Riemann-Roch theorem
- Grothendieck-Riemann-Roch theorem
- Coherent duality
[edit] Schemes
- Affine scheme
- Scheme
- Glossary of scheme theory
- Éléments de géométrie algébrique
- Grothendieck's Séminaire de géométrie algébrique
- Flat morphism
- Finite morphism
- Quasi-finite morphism
- Group scheme
- Semistable elliptic curve
- Grothendieck's relative point of view
[edit] Category theory
- Grothendieck topology
- Topos
- Descent (category theory)
- Algebraic stack
- Gerbe
- Etale cohomology
- Motive (mathematics)
- Motivic cohomology
- Homotopical algebra
[edit] Algebraic geometers
- Niels Henrik Abel
- Carl Gustav Jakob Jacobi
- Jakob Steiner
- Julius Plücker
- Bernhard Riemann
- William Kingdon Clifford
- Italian school of algebraic geometry
- Solomon Lefschetz
- Oscar Zariski
- Erich Kähler
- W. V. D. Hodge
- Kunihiko Kodaira
- André Weil
- Jean-Pierre Serre
- Alexander Grothendieck
- David Mumford
- Igor Shafarevich
- Heisuke Hironaka
- Shigefumi Mori
- Vladimir Voevodsky
