 List of algebraic geometry topics

This is a list of algebraic geometry topics, by Wikipedia page.
Contents
Classical topics in projective geometry
 Affine space
 Projective space
 Projective line, crossratio
 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, multiway projective space
 Rational normal curve
Algebraic curves
 Conics, Pascal's theorem, Brianchon's theorem
 Twisted cubic
 Elliptic curve, cubic curve
 Hyperelliptic curve
 Klein quartic
 modular curve
 modular equation
 modular function
 modular group
 Supersingular primes
 Fermat curve
 Bézout's theorem
 Brill–Noether theory
 Edwards curve
 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
Algebraic surfaces
 EnriquesKodaira 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
 Tangent space, Zariski tangent space
 Function field
 Ample vector bundle
 Linear system of divisors
 Birational geometry
 Blowing up
 Rational variety
 Unirational variety
 Intersection number
 Intersection theory
 Serre's multiplicity conjectures
 Albanese variety
 Picard group
 Pluricanonical ring
 Modular form
 Moduli space
 Modular equation
 Algebraic function
 Algebraic form
 Addition theorem
 Invariant theory
 Symbolic method of invariant theory
 Geometric invariant theory
 Toric geometry
 Deformation theory
 Singular point, nonsingular
 Singularity theory
 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
 Identity component
 Linear algebraic group
 Additive group
 Multiplicative group
 Borel subgroup
 Parabolic subgroup
 Radical of an algebraic group
 Unipotent radical
 LieKolchin theorem
 Mumford conjecture
 Abelian variety
 Grassmannian
 Flag manifold
 Algebraic torus
 Weil restriction
 Differential Galois theory
Contemporary foundations
Main article glossary of scheme theory
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
 Generic flatness
 Irrelevant ideal
Sheaf theory
 Locally ringed space
 Coherent sheaf
 Invertible sheaf
 Sheaf cohomology
 Hirzebruch–Riemann–Roch theorem
 Grothendieck–Riemann–Roch theorem
 Coherent duality
 Dévissage
Schemes
 Affine scheme
 Scheme
 Glossary of scheme theory
 Éléments de géométrie algébrique
 Grothendieck's Séminaire de géométrie algébrique
 Flat morphism
 Finite morphism
 Quasifinite morphism
 Group scheme
 Semistable elliptic curve
 Grothendieck's relative point of view
Category theory
 Grothendieck topology
 Topos
 Descent (category theory)
 Algebraic stack
 Gerbe
 Étale cohomology
 Motive (mathematics)
 Motivic cohomology
 Homotopical algebra
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
 JeanPierre Serre
 Alexander Grothendieck
 David Mumford
 Igor Shafarevich
 Heisuke Hironaka
 Shigefumi Mori
 Vladimir Voevodsky
Categories: Mathematicsrelated lists
 Algebraic geometry
 Outlines
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