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, multi-way projective space *Rational normal curve

=Algebraic curves=

*Conics, Pascal s theorem, Brianchon s theorem *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 prime *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=

*Ruled surface *Cubic surface *Veronese surface *Del Pezzo surface *K3 surface *Hodge index theorem *Surface of general type

=Algebraic geometry: classical approach=

*Algebraic variety **Hypersurface **Quadric **Dimension of an algebraic variety **Hilbert s Nullstellensatz **Complete variety **Elimination theory **Quasiprojective variety ***Gröbner basis **Canonical bundle **Serre duality **Arithmetic genus, geometric genus, irregularity *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 **J-invariant *Algebraic function *Algebraic form *Addition theorem *Invariant theory **Symbolic method of invariant theory *Geometric invariant theory *Toric geometry *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=

*Identity component *Linear algebraic group **Additive group **Multiplicative group **Borel subgroup **Parabolic subgroup **Radical of an algebraic group **Unipotent radical **Lie-Kolchin theorem **Mumford conjecture *Abelian variety **Theta function *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 (mathematics) *Glossary of scheme theory *�léments de géométrie algébrique *Grothendieck s Séminaire de géométrie algébrique *Flat morphism *Finite morphism *Quasi-finite morphism *Group scheme *Semistable elliptic curve *Grothendieck s relative point of view

==Category theory==

*Grothendieck topology *Topos *Descent (category theory) **Grothendieck s Galois 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 **Guido Castelnuovo **Francesco Severi *Solomon Lefschetz *Oscar Zariski *Erich Kähler *W. V. D. Hodge *Kunihiko Kodaira *André Weil *Jean-Pierre Serre *Alexander Grothendieck *David Mumford *Igor Shafarevich *Heisuke Hironaka *Shigefumi Mori *Vladimir Voevodsky