Algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commut... Algebraic geometry - Wikipedia
 Universal algebraic geometry - Slideshow
 Deligne conjecture - Slideshow
 Rational mapping In mathematics, in particular the subfield of algebraic geometry, a rational map is a kind of partial function between algebraic varieties. This article uses the convention that varieties are irreduc...
 Algebraic geometry of projective spaces Projective space plays a central role in algebraic geometry. The aim of this article is to define the notion in terms of abstract algebraic geometry and to describe some basic uses of projective space... Algebraic geometry of projective spaces - Wikipedia
 Theorems in algebraic geometry
 Algebraic geometers Algebraic geometers - Wikipedia
 Algebraic curve In mathematics, an algebraic curve or plane algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.For example, the unit circle is ... Algebraic curve - Wikipedia
 Algebraic variety In mathematics, algebraic varieties (also called varieties) are one of the central objects of study in algebraic geometry. Classically, an algebraic variety was defined to be the set of solutions of a...
 Analytic geometry In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.Analyt... Analytic geometry - Wikipedia
 Birational geometry In algebraic geometry, the goal of birational geometry is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given b...
 Cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex. That is, cohomology is defined a...
 Diophantine geometry In mathematics, diophantine geometry is one approach to the theory of Diophantine equations, formulating questions about such equations in terms of algebraic geometry over a ground field K that is not...
 Intersection theory In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within th... Intersection theory - Wikipedia
 Invariant theory Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the the...
 Localization Localization or localisation may refer to:
 Moduli space In algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such... Moduli space - Wikipedia
 Noncommutative geometry Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutativ...
 Real algebraic geometry In mathematics, real algebraic geometry is the study of real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular r...
 Scheme (mathematics) In mathematics, schemes connect the fields of algebraic geometry, commutative algebra and number theory. Schemes were introduced by Alexander Grothendieck in 1960 in his treatise Éléments de géométrie...
 Singularity theory In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity...
 Structures on manifolds
 Topological methods of algebraic geometry
 Kodaira vanishing theorem In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indice...
 BRST quantization In theoretical physics, BRST quantization (where the BRST refers to Becchi, Rouet, Stora and Tyutin) denotes a relatively rigorous mathematical approach to quantizing a field theory with a gauge symme...
 Spherical variety
 Quotient stack
 André–Oort conjecture
 Scorza variety
 Noncommutative algebraic geometry Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry that studies the geometric properties of formal duals of non-commutative alge...
 Jean-Pierre Serre Jean-Pierre Serre ([sɛʁ]; born 15 September 1926) is a French mathematician who has made fundamental contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarde... Jean-Pierre Serre - Wikipedia