Search for "Algebraic geometry" in article titles:

1. Algebraic geometry: Classical algebraic geometry is the study of geometric properties of the objects defined by algebraic equations. For example, a parabola, such as all solutions ( x , y ) {\displaystyle (x,y)} of the equation y − x 2 = 0 {\displaystyle y-x^{2 ... [100%] 2023-06-17
2. Algebraic geometry: The branch of mathematics dealing with geometric objects connected with commutative rings: algebraic varieties (cf. Algebraic variety) and their various generalizations (schemes, algebraic spaces, etc., cf. (Mathematics) [100%] 2023-09-08
3. Algebraic geometry: Algebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. (Branch of mathematics) [100%] 2023-09-06 [Algebraic geometry] [Fields of mathematics]...
4. Algebraic geometry: Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. (Branch of mathematics) [100%] 2024-11-13 [Algebraic geometry]
5. Algebraic geometry and analytic geometry: In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several ... (Two closely related mathematical subjects) [63%] 2023-08-23 [Algebraic geometry] [Analytic geometry]...
6. Divisor (algebraic geometry): In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common use, Cartier divisors and Weil divisors (named for Pierre Cartier and André Weil by David Mumford). (Algebraic geometry) [81%] 2023-11-13 [Geometry of divisors]
7. Numerical algebraic geometry: Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical analysis to study and manipulate the solutions of systems of polynomial equations. The primary computational method used in numerical algebraic geometry is ... [81%] 2024-01-09 [Algebraic geometry] [Computational geometry]...
8. Motive (algebraic geometry): In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast array of similarly behaved cohomology theories such as singular cohomology, de Rham cohomology, etale cohomology, and ... (Algebraic geometry) [81%] 2023-12-28 [Algebraic geometry] [Topological methods of algebraic geometry]...
9. Torsor (algebraic geometry): In algebraic geometry, a torsor or a principal bundle is an analog of a principal bundle in algebraic topology. Because there are few open sets in Zariski topology, it is more common to consider torsors in étale topology or some ... (Algebraic geometry) [81%] 2023-12-21 [Algebraic geometry]
10. Real algebraic geometry: In mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomial mappings). [81%] 2023-12-18 [Real algebraic geometry]
11. 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 algebraic objects such as rings as well as geometric objects derived from them ... [81%] 2023-09-06 [Algebraic geometry] [Noncommutative geometry]...
12. Divisor (algebraic geometry): In geometry a divisor on an algebraic variety is a formal sum (with integer coefficients) of subvarieties. An effective divisor is a sum with non-negative integer coefficients. (Algebraic geometry) [81%] 2023-07-09
13. Torsor (algebraic geometry): In algebraic geometry, a torsor or a principal bundle is an analogue of a principal bundle in algebraic topology. Because there are few open sets in Zariski topology, it is more common to consider torsors in étale topology or some ... (Algebraic geometry) [81%] 2024-02-13 [Algebraic geometry]
14. Purity (algebraic geometry): In the mathematical field of algebraic geometry, purity is a theme covering a number of results and conjectures, which collectively address the question of proving that "when something happens, it happens in a particular codimension". For example, ramification is a ... (Algebraic geometry) [81%] 2023-12-19 [Algebraic geometry]
15. Divisor (algebraic geometry): In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common use, Cartier divisors and Weil divisors (named for Pierre Cartier and André Weil by David Mumford). (Algebraic geometry) [81%] 2023-12-10 [Geometry of divisors]
16. Degeneration (algebraic geometry): In algebraic geometry, a degeneration (or specialization) is the act of taking a limit of a family of varieties. Precisely, given a morphism of a variety (or a scheme) to a curve C with origin 0 (e.g., affine or ... (Algebraic geometry) [81%] 2023-05-17 [Algebraic geometry]
17. Period (algebraic geometry): 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 periods remain periods, so the periods form a ring. (Algebraic geometry) [81%] 2023-11-11 [Mathematical constants] [Algebraic geometry]...
18. Quadric (algebraic geometry): In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. (Algebraic geometry) [81%] 2023-10-18 [Quadrics] [Algebraic geometry]...
19. Discrepancy (algebraic geometry): In algebraic geometry, given a pair (X, D) consisting of a normal variety X and a \displaystyle{ \mathbb{Q} }[/math]-divisor D on X (e.g., canonical divisor), the discrepancy of the pair (X, D) measures the degree of the ... (Algebraic geometry) [81%] 2023-09-22 [Algebraic geometry]
20. Cone (algebraic geometry): In algebraic geometry, a cone is a generalization of a vector bundle. Specifically, given a scheme X, the relative Spec of a quasi-coherent graded OX-algebra R is called the cone or affine cone of R. (Algebraic geometry) [81%] 2023-11-17 [Algebraic geometry] [Vector bundles]...
21. Quadric (algebraic geometry): In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. (Algebraic geometry) [81%] 2022-10-09 [Quadrics] [Algebraic geometry]...
22. Differential algebraic geometry: Differential algebraic geometry is an area of differential algebra that adapts concepts and methods from algebraic geometry and applies them to systems of differential equations, especially algebraic differential equations. Another way of generalizing ideas from algebraic geometry is diffiety theory. [81%] 2023-12-04 [Differential algebra]
23. Convexity (algebraic geometry): In algebraic geometry, convexity is a restrictive technical condition for algebraic varieties originally introduced to analyze Kontsevich moduli spaces M ¯ 0 , n ( X , β ) {\displaystyle {\overline {M}}_{0,n}(X,\beta )} in quantum cohomology.These moduli spaces are smooth orbifolds ... (Algebraic geometry) [81%] 2022-02-11 [Algebraic geometry]
24. Cone (algebraic geometry): In algebraic geometry, a cone is a generalization of a vector bundle. Specifically, given a scheme X, the relative Spec of a quasi-coherent graded OX-algebra R is called the cone or affine cone of R. (Algebraic geometry) [81%] 2023-12-28 [Algebraic geometry] [Vector bundles]...
25. Divisor (algebraic geometry): For other meanings of the term 'Divisor' see the page Divisor (disambiguation) In algebraic geometry, the term divisor is used as a generalization of the concept of a divisor of an element of a commutative ring. First introduced by E ... (Mathematics) [81%] 2023-12-10
26. Numerical algebraic geometry: Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical analysis to study and manipulate the solutions of systems of polynomial equations. The primary computational method used in numerical algebraic geometry is ... [81%] 2024-04-05 [Algebraic geometry] [Computational geometry]...
27. Geometrically (algebraic geometry): In algebraic geometry, especially in scheme theory, a property is said to hold geometrically over a field if it also holds over the algebraic closure of the field. In other words, a property holds geometrically if it holds after a ... (Algebraic geometry) [81%] 2024-08-16 [Scheme theory]
28. Correspondence (algebraic geometry): 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, a subset of a Cartesian product of two sets is called a ... (Algebraic geometry) [81%] 2024-06-12 [Algebraic geometry]
29. Abstract algebraic geometry: The branch of algebraic geometry dealing with the general properties of algebraic varieties (cf. Algebraic variety) over arbitrary fields and with schemes (cf. (Mathematics) [81%] 2024-07-24
30. Derived noncommutative algebraic geometry: In mathematics, derived noncommutative algebraic geometry, the derived version of noncommutative algebraic geometry, is the geometric study of derived categories and related constructions of triangulated categories using categorical tools. Some basic examples include the bounded derived category of coherent sheaves ... [70%] 2023-12-18 [Algebraic geometry] [Noncommutative geometry]...