Linked from

The 40 pages that link to Algebraic geometry, each with the reason it gives.

• Differential geometryCompared with: It often builds geometry from algebraic equations rather than differential calculus.

• Incidence geometryRelated: Algebraic geometry supplies varieties and polynomial tools for incidence problems.

• Polynomial ringNarrower topic: Polynomial rings supply the equations and coordinate algebras used to describe varieties.

• Analytic geometryNarrower topic: It generalizes the equation-and-shape connection to systems of polynomial equations.

• TrigonometryCompared with: It provides a contrasting framework for equations that trigonometric substitution can transform.

• André WeilNarrower topic: Weil used geometric methods to expose structure in number-theoretic problems.

• Abstract algebraRelated: It links commutative rings and fields to geometric spaces and their properties.

• Arthur CayleyRelated: Cayley’s research on curves and surfaces contributed to the nineteenth-century development of algebraic geometry.

• Synthetic geometryCompared with: It reverses the classical emphasis by making equations the starting point for geometry.

• Quotient ringNarrower topic: Coordinate rings translate polynomial equations into ideals and quotient rings.

• Commutative ringRelated: Its affine spaces are built from commutative rings through their prime ideals.

• Algebraic closureRelated: Algebraically closed fields provide natural coefficient fields for geometric results about polynomial solutions.

• Commutative algebraRelated: Commutative rings provide coordinate algebras for affine algebraic geometry.

• Polynomial equationNarrower topic: Polynomial equations define the varieties that are central objects in this field.

• Hilbert's NullstellensatzNarrower topic: The theorem became a foundational bridge between this field’s equations and its geometric objects.

• Noetherian ringNarrower topic: Noetherian coordinate rings enable finite descriptions of algebraic varieties and their subspaces.

• Riemann–Roch theoremNarrower topic: The theorem became a foundational bridge between curve geometry and function spaces.

• Jean-Pierre SerreNarrower topic: Serre’s sheaf-theoretic foundations helped prepare the subject for its modern form.

• Algebraically closed fieldNarrower topic: Its classical theory often takes an algebraically closed field as the base field.

• History of algebraCompared with: It reverses the historical traffic between algebra and geometry by using equations to study shapes.

• Abelian varietyNarrower topic: Abelian varieties grew from algebraic geometry’s effort to understand curves and their divisor classes.

• Singularity theoryNarrower topic: Its methods classify singular points of curves, surfaces, and higher-dimensional varieties.

• Geometric analysisCompared with: It shares geometric questions but emphasizes algebraic structure over analytic estimates.

• History of geometryRelated: It developed from analytic geometry into a major meeting point of geometry and algebra.

• Algebraic functionNarrower topic: It studies the curves and higher-dimensional varieties underlying algebraic functions.

• Arithmetic geometryNarrower topic: Its geometric language supplies the varieties and schemes studied arithmetically.

• Hodge conjectureNarrower topic: The conjecture asks whether certain topological classes have algebraic representatives.

• Ring theoryRelated: Coordinate rings translate polynomial geometry into ring structure.

• Serge LangNarrower topic: It was a major field in Lang’s research, especially through his work on abelian varieties.

• Cayley–Bacharach theoremNarrower topic: The result became a central relation between polynomial equations and intersection geometry.

• Jean DieudonnéNarrower topic: Dieudonné contributed to its foundations and helped make its modern language accessible.

• Kunihiko KodairaNarrower topic: Kodaira connected algebraic methods with the analysis of complex manifolds.

• Ngô Bảo ChâuNarrower topic: Geometric methods made the fundamental lemma accessible through moduli spaces and their fibers.

• Ax–Grothendieck theoremNarrower topic: The theorem is a foundational rigidity statement in this field.

• Bogomolov–Miyaoka–Yau inequalityNarrower topic: Bogomolov’s and Miyaoka’s approaches place the inequality within the classification of algebraic surfaces.

• Charlotte ScottRelated: Scott’s research centered on algebraic curves and their properties.

• Claire VoisinNarrower topic: This is the broad mathematical field in which Voisin made her career.

• Corrado SegreNarrower topic: Segre helped shape this field through systematic study of varieties and their projective embeddings.

• Harnack's curve theoremNarrower topic: Harnack's theorem is a landmark result connecting algebraic equations with real topology.

• Shigefumi MoriNarrower topic: Mori’s research developed within this broad field.