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 curves

 * 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 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

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 manifolds

 * Kähler manifold
 * Calabi–Yau manifold
 * Stein manifold
 * Hodge theory
 * Hodge cycle
 * Hodge conjecture
 * Algebraic geometry and analytic geometry
 * Mirror symmetry

Algebraic groups

 * 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 (also known as the Mumford conjecture)
 * Group scheme
 * Abelian variety
 * Theta function
 * Grassmannian
 * Flag manifold
 * Weil restriction
 * Differential Galois theory

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