List of algebraic geometry topics
This is a list of algebraic geometry topics, by Wikipedia page.
Classical topics in [projective geometry]
- Affine space
- Projective space
- Projective line, cross-ratio
- Projective plane
- *Line at infinity
- *Complex 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 of a product of projective spaces
- Rational normal curve
[Algebraic curve]s
- Conics, Pascal's theorem, Brianchon's theorem
- Twisted cubic
- Elliptic curve, cubic curve
- *Elliptic function, Jacobi's elliptic functions, Weierstrass's elliptic functions
- *Elliptic integral
- *Complex multiplication
- *Weil pairing
- Hyperelliptic curve
- Klein quartic
- Modular curve
- *Modular equation
- *Modular function
- *Modular group
- *Supersingular primes
- 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
- *Generalized Jacobian
- Moduli of algebraic curves
- Hurwitz's theorem on automorphisms of a curve
- Clifford's theorem on special divisors
- Gonality of an algebraic curve
- Weil reciprocity law
- Algebraic geometry codes
[Algebraic surface]s
- 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
Algebraic geometry: classical approach
- Algebraic variety
- *Hypersurface
- *Quadric (algebraic geometry)
- *Dimension of an algebraic variety
- *Hilbert's Nullstellensatz
- *Complete variety
- *Elimination theory
- *Gröbner basis
- *Projective variety
- *Quasiprojective variety
- *Canonical bundle
- *Complete intersection
- *Serre duality
- *Spaltenstein variety
- *Arithmetic genus, geometric genus, irregularity
- Tangent space, Zariski tangent space
- Function field of an algebraic variety
- Ample line bundle
- Ample vector bundle
- Linear system of divisors
- Birational geometry
- *Blowing up
- *Resolution of singularities
- *Rational variety
- *Unirational variety
- *Ruled variety
- *Kodaira dimension
- *Canonical ring
- *Minimal model program
- Intersection theory
- *Intersection number
- *Chow ring
- *Chern class
- *Serre's multiplicity conjectures
- Albanese variety
- Picard group
- Modular form
- Moduli space
- Modular equation
- *J-invariant
- Algebraic function
- Algebraic form
- Addition theorem
- Invariant theory
- *Symbolic method of invariant theory
- Geometric invariant theory
- Toric variety
- Deformation theory
- Singular point, non-singular
- Singularity theory
- *Newton polygon
- Weil conjectures
[Complex manifold]s
- Kähler manifold
- Calabi–Yau manifold
- Stein manifold
- Hodge theory
- Hodge cycle
- Hodge conjecture
- Algebraic geometry and analytic geometry
- Mirror symmetry
[Algebraic group]s
- Linear algebraic group
- *Additive group
- *Multiplicative group
- *Algebraic torus
- *Reductive group
- *Borel subgroup
- *Radical of an algebraic group
- *Unipotent radical
- *Lie-Kolchin theorem
- *Haboush's theorem
- Group scheme
- Abelian variety
- *Theta function
- Grassmannian
- Flag manifold
- Weil restriction
- Differential Galois theory
Contemporary foundations
[Commutative algebra]
- Prime ideal
- Valuation (algebra)
- Krull dimension
- Regular local ring
- Regular sequence
- Cohen-Macaulay ring
- Gorenstein ring
- Koszul complex
- Spectrum of a ring
- Zariski topology
- Kähler differential
- Generic flatness
- Irrelevant ideal
[Sheaf theory]
- Locally ringed space
- Coherent sheaf
- Invertible sheaf
- Sheaf cohomology
- Coherent sheaf cohomology
- Hirzebruch–Riemann–Roch theorem
- Grothendieck–Riemann–Roch theorem
- Coherent duality
- Dévissage
Schemes
- Affine scheme
- Scheme
- Éléments de géométrie algébrique
- Grothendieck's Séminaire de géométrie algébrique
- Fiber product of schemes
- Flat morphism
- Smooth scheme
- Finite morphism
- Quasi-finite morphism
- Proper morphism
- Semistable elliptic curve
- Grothendieck's relative point of view
- Hilbert scheme
[Category theory]
- Grothendieck topology
- Topos
- Derived category
- Descent (category theory)
- *Grothendieck's Galois theory
- Algebraic stack
- Gerbe
- Étale cohomology
- Motive (algebraic geometry)
- Motivic cohomology
- A¹ homotopy theory
- Homotopical algebra
Algebraic geometers
- Niels Henrik Abel
- Carl Gustav Jacob Jacobi
- Jakob Steiner
- Julius Plücker
- Arthur Cayley
- Bernhard Riemann
- Max Noether
- William Kingdon Clifford
- David Hilbert
- Italian school of algebraic geometry
- *Guido Castelnuovo
- *Federigo Enriques
- *Francesco Severi
- Solomon Lefschetz
- Oscar Zariski
- W. V. D. Hodge
- Sir Michael Atiyah
- Kunihiko Kodaira
- André Weil
- Jean-Pierre Serre
- Alexander Grothendieck
- Friedrich Hirzebruch
- Igor Shafarevich
- Heisuke Hironaka
- Shreeram S. Abhyankar
- Pierre Samuel
- C.P. Ramanujam
- David Mumford
- Michael Artin
- Phillip Griffiths
- Pierre Deligne
- Yuri Manin
- Shigefumi Mori
- Vladimir Drinfeld
- Vladimir Voevodsky
- Claire Voisin
- János Kollár
- Caucher Birkar
- Burt Totaro
- Patrick Brosnan
- Robin Hartshorne
- Joe Harris