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Algebraic geometry

Definitions and resources

ScienceWISE definitions	External resources
	Algebraic geometry by Wikipedia Algebraic geometry by Internet Encyclopedia of Science

Semantic relations

Incoming relations	Outgoing relations
	Algebraic geometry is a part of Algebraic geometry and analytic geometry Algebraic geometry is important in String theory

Subcategories and concepts

Subcategories

Concepts

Hopf fibration Atiyah-Singer index theorem Automorphism Epimorphism Homomorphism Lie group homomorphism Monomorphism Normal morphism Order isomorphism Zero morphism Algebraic K-theory Algebraic set Ground field Residue field Unibranch local ring 3-fold Abel's curve theorem Abhyankar's lemma Abhyankar-Moh theorem Abstract algebraic variety Addition theorem Adequate equivalence relation Adjunction formula AF+BG theorem Algebraic cycle Algebraic geometry of projective spaces Algebraic space Algebraic variety Anabelian geometry Analytic geometry Analytic space Arakelov theory Arithmetic and geometric Frobenius Arithmetic group A¹ homotopy theory Baily-Borel compactification Barsotti-Tate group Base locus Bézout's theorem Biholomorphism Biregular Borel fixed-point theorem Buchberger's algorithm Canonical ring Canonical singularity Castelnuovo-Mumford regularity Catenary ring Chow coordinates Chow ring Codimension Cohen-Macaulay ring Combinatorial commutative algebra Complete intersection Complex analytic space Complex dimension Cone of curves Conic bundle Constructible set Constructible sheaf Crepant resolution Deligne conjecture Determinantal variety Dévissage Differential of the first kind Drinfel'd module Du Bois singularity Dwork family Elimination theory Enneper surface Equidimensional scheme Erdős-Diophantine graph Esquisse d'un Programme Euler sequence Excellent ring Exceptional divisor Fake projective space Fano fibration Fano variety Finite morphism Flat function Flat topology Formal scheme Formally smooth map Fourier-Deligne transform Fujiki class C Fujita conjecture Galois geometry General position Generalized Jacobian Generic flatness Generic point Grauert-Riemenschneider vanishing theorem Gröbner basis Grothendieck's connectedness theorem H topology Hessenberg variety Hilbert's arithmetic of ends Hilbert's fifteenth problem Hitchin system Homogeneous polynomial Hyperplane section Inverse image functor Irreducible component Irrelevant ideal Jacobian conjecture Kawamata-Viehweg vanishing theorem Kodaira embedding theorem Kähler differential Lefschetz theorem on Locally free sheaf Logarithmic pair Max Noether's theorem Milnor number Mnev's universality theorem Mori dream space Motivic L-function Motivic zeta function Multiplicative distance Mumford vanishing theorem Nagata ring Nakai conjecture Nakayama lemma Nash blowing-up Néron-Severi group Nisnevich topology Noetherian topological space Noncommutative algebraic geometry Normal crossings Plucker matrix Pseudo algebraically closed field Quasi-homogeneous polynomial Ramanujam vanishing theorem Rational mapping Rees algebra Regular chain Regular semi-algebraic system Relative canonical model Relative dimension Resolution of singularities Riemann-Roch theorem for algebraic curves Ring of periods Ruled variety Schubert calculus Secant variety Shriek map Stable vector bundle Syntomic topology Tangent cone Terminal singularity Toric variety Triangular decomposition Trivial cylinder Tropical geometry Tsen's theorem Universal algebraic geometry Valuative criterion Vanishing theorem Wu's method of characteristic set Zariski space Zariski tangent space Zariski's main theorem Zariski-Riemann space Étale topology Alexander-Spanier cohomology Brown-Peterson cohomology Čech cohomology Cohomology with compact support De Rham cohomology Dolbeault cohomology Elliptic cohomology Intersection homology Morava K-theory Motivic cohomology Spencer cohomology Steenrod homology Topological modular forms Weil cohomology theory Andreotti-Frankel theorem Arithmetic genus Coherent duality Coherent sheaf Essentially finite vector bundle Étale fundamental group Fundamental group scheme Genus of a multiplicative sequence Grothendieck-Hirzebruch-Riemann-Roch theorem Hirzebruch-Riemann-Roch theorem Homotopical algebra Kodaira vanishing theorem Lefschetz hyperplane theorem Serre duality Sheaf spanned by global sections Tate conjecture Vanishing cycle Abstract variety Algebraic manifold Branched covering Coble variety Complete algebraic variety Complex projective space Cubic form Cubic threefold Degree of an algebraic variety Function field of an algebraic variety Geometric genus Hermitian variety Hilbert's Nullstellensatz Homogeneous coordinate ring Irreducible variety Line complex Nef line bundle Noether normalization lemma Norm variety Quasiprojective variety Quintic threefold Rational function Rational variety Reducible variety Regular function Segre embedding Singular point of an algebraic variety Stengle's Positivstellensatz Theorem of the cube Transcendence degree Weil restriction Zariski surface Zariski topology Differential form

General information

Categorization	Also known as
Mathematics (under construction)

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