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
Goppa code

Algebraic surfaces

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
- 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

Algebraic groups

Linear algebraic group
- Additive group
- Multiplicative group
- Algebraic torus
- Reductive group
- Borel subgroup
- Parabolic 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

Contemporary foundations

Commutative algebra

Sheaf theory

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

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