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...

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...

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

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...

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

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

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

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

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

algebraic geometry, a period or algebraic period is a complex number that can be expressed as an integral of an algebraic function over an algebraic domain...

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

classical algebraic geometry of varieties over algebraically closed fields. This chapter uses many classical results in commutative algebra, including...

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...

mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has...

of general type Zariski surface Algebraic variety Hypersurface Quadric (algebraic geometry) Dimension of an algebraic variety Hilbert's Nullstellensatz...

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

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

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...

2024. Danilov, V. I. (2006). "II. Algebraic Varieties and Schemes". Algebraic Geometry I: Algebraic Curves, Algebraic Manifolds and Schemes. Springer....

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

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

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

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

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

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...

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...