Category:Algebraic geometry

*

• [+] Algebraic geometers (47 P)

A

• [+] Algebraic varieties (7 C, 40 P)

C

• [+] Cohomology theories (23 P)

D

• [+] Diophantine geometry (27 P)

I

• [+] Intersection theory (9 P)

I cont.

• [+] Invariant theory (1 C, 26 P)

L

• [+] Localization (mathematics) (10 P)

M

• [+] Moduli theory (1 C, 13 P)

R

• [+] Real algebraic geometry (10 P)

S

• [+] Scheme theory (1 C, 24 P)

S cont.

• [+] Singularity theory (2 C, 39 P)
• [+] Surfaces (6 C, 99 P, 1 F)

T

• [+] Topological methods of algebraic geometry (34 P)

• List of algebraic geometry topics
• Glossary of arithmetic and Diophantine geometry

*

• Algebraic geometry
• Rational point
• Residue field

3

• 3-fold

A

• AF+BG theorem
• Abel's curve theorem
• Abhyankar's lemma
• Abhyankar–Moh theorem
• Absolutely irreducible
• Abstract algebraic variety
• Addition theorem
• Adjunction formula (algebraic geometry)
• Affine Grassmannian
• Affine Grassmannian (manifold)
• Algebraic K-theory
• Algebraic cycle
• Algebraic geometry and analytic geometry
• Algebraic set
• Algebraic space
• Algebraic stack
• Algebraic variety
• Amoeba (mathematics)
• Ample line bundle
• Analytic geometry
• Analytic space
• Analytic variety
• Arakelov theory
• Arithmetic and geometric Frobenius
• Arithmetic group
• A¹ homotopy theory

B

• Baily–Borel compactification
• Base locus
• Bézout's theorem
• Biholomorphism
• Borel fixed-point theorem

C

• Calabi–Yau manifold
• Canonical ring
• Canonical singularity
• Castelnuovo–Mumford regularity
• Catenary ring
• Characteristic set
• Chow coordinates
• Chow ring
• Codimension
• Cohen–Macaulay ring
• Combinatorial commutative algebra
• Complete intersection
• Complex analytic space
• Complex dimension
• Cone of curves
• Conic bundle
• Conifold
• Cotangent complex
• Cramer's paradox
• Crepant resolution
• Crystalline cohomology

D

• Deformation theory
• Deligne conjecture
• Descent (category theory)
• Dessin d'enfant
• Determinantal variety

D cont.

• Differential of the first kind
• Direction cosine
• Drinfel'd module
• Du Bois singularity

E

• Elimination theory
• Enneper surface
• Equivalence relations on algebraic cycles
• Erdős–Diophantine graph
• Esquisse d'un Programme
• Euler sequence
• Excellent ring
• Exceptional divisor

F

• Fake projective space
• Family of curves
• Fano fibration
• Fano variety
• Field with one element
• Finite morphism
• Flat module
• Flat topology
• Flip (algebraic geometry)
• Formal scheme
• Fujiki class C
• Fujita conjecture

G

• Galois geometry
• Gauss–Manin connection
• General elephant
• Generalized Jacobian
• Generalized Riemann hypothesis
• Generic point
• Generic property
• Genus degree formula
• Grassmannian
• Grauert–Riemenschneider vanishing theorem
• Gröbner basis
• Gromov–Witten invariant
• Grothendieck connection
• Grothendieck's Galois theory
• Grothendieck's connectedness theorem
• Grothendieck–Katz p-curvature conjecture

H

• Hasse–Weil zeta function
• Hessenberg variety
• Hilbert scheme
• Hilbert's arithmetic of ends
• Hilbert's fifteenth problem
• Hitchin system
• Hodge structure
• Homogeneous polynomial
• Homological algebra
• Hyperkähler manifold
• Hyperplane section
• Hypersurface

I

• Injective sheaf
• Inverse image functor
• Irreducible component
• Italian school of algebraic geometry

J

• Jacobian conjecture

K

• Kähler differential
• Kähler manifold
• Kawamata–Viehweg vanishing theorem
• Kodaira embedding theorem

L

• LLT polynomial
• Local parameter

L cont.

• Locally free sheaf
• Logarithmic form
• Logarithmic pair

M

• Macdonald polynomial
• Max Noether's theorem
• Milnor number
• Minimal model program
• Mnev's universality theorem
• Mori dream space
• Motivic integration
• Multiplicative distance
• Mumford vanishing theorem
• Mysterious duality

N

• N!-conjecture
• Nagata ring
• Nakai conjecture
• Nakayama lemma
• Néron model
• Néron–Tate height
• Noetherian topological space
• Noncommutative algebraic geometry
• Noncommutative quotients
• Normal crossings
• Néron–Severi group

P

• Pencil (mathematics)
• Period (number)
• Plücker embedding
• Positive form
• Projective algebraic manifold
• Pseudo algebraically closed field
• Pseudoholomorphic curve

Q

• Quantum cohomology
• Quasi-homogeneous polynomial

R

• Ramanujam vanishing theorem
• Rational mapping
• Regular local ring
• Regular map (algebraic geometry)
• Relative canonical model
• Relative dimension
• Resolution of singularities
• Ruled variety

S

• Schubert calculus
• Schubert variety
• Sheaf extension
• Shimura variety
• Shriek map
• Smooth function
• Stable vector bundle
• Stack (descent theory)
• Standard conjectures on algebraic cycles

T

• Tangent cone
• Terminal singularity
• Theorem of Bertini
• Toric geometry
• Tropical geometry
• Tsen's theorem

U

• Universal algebraic geometry

V

• Valuation (algebra)
• Valuative criterion
• Vanishing theorem

W

• Wall-crossing