List of algebraic geometry topics
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This is a list of algebraic geometry topics, by Wikipedia page.
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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
Algebraic curves
- Conics, Pascal's theorem, Brianchon's theorem
- 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
Algebraic surfaces
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
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
- 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
Sheaf theory
- Locally ringed space
- Coherent sheaf
- Invertible sheaf
- Sheaf cohomology
- Grothendieck-Riemann-Roch theorem
- Coherent duality
Schemes
- Affine scheme
- Scheme
- Glossary of scheme theory
- Éléments de géométrie algébrique
- Grothendieck's Séminaire de géométrie algébrique
- Flat morphism
- Group scheme
- Semistable elliptic curve
- Grothendieck's relative point of view
Category theory
- Grothendieck topology
- Topos
- Descent (category theory)
- Algebraic stack
- Gerbe
- Etale cohomology
- Motive (mathematics)
- Motivic cohomology
- Homotopical algebra
The 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
- André Weil
- Jean-Pierre Serre
- Alexander Grothendieck
- Igor Shafarevich
- Heisuke Hironaka
- Shigefumi Mori
- Vladimir Voevodsky