Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc.—or...

algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals...

This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory...

In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast...

arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around...

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...

models not describable via linear algebra. This period in geometry was overtaken by research on the general algebraic curve by Clebsch, Riemann, Max Noether...

mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with...

In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common...

Algebraic geometry codes, often abbreviated AG codes, are a type of linear code that generalize Reed–Solomon codes. The Russian mathematician V. D. Goppa...

optimizing departure times for a network of trains. Tropical geometry is a variant of algebraic geometry in which polynomial graphs resemble piecewise linear...

transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis. Complex geometry sits at the intersection...

In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in...

Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local...

Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric...

classes of algebraic structures. Algebraic methods were first studied in the ancient period to solve specific problems in fields like geometry. Subsequent...

commutative algebra can be viewed as an algebraic approach to affine algebraic varieties. However, many arguments in algebraic geometry work better for...

mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became...

of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory...

continuous deformations. Algebraic topology, the use in topology of algebraic methods, mainly homological algebra. Discrete geometry, the study of finite...

In algebraic geometry, a period is a number that can be expressed as an integral of an algebraic function over an algebraic domain. Sums and products of...

equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than...

In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside...

reconstructed from the Banach algebra of functions on the space (Gelfand–Naimark). In commutative algebraic geometry, algebraic schemes are locally prime...

universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...

as π that are not algebraic are said to be transcendental. Almost all real and complex numbers are transcendental. Algebraic geometry is a branch of mathematics...

occurring in algebraic number theory and algebraic geometry. Several concepts of commutative algebras have been developed in relation with algebraic number...

In algebraic geometry, a correspondence between algebraic varieties V and W is a subset R of V×W, that is closed in the Zariski topology. In set theory...

Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Combinatorial geometry Computational geometry Conformal...