[go: up one dir, main page]

Algebraic geometry

branch of mathematics dealing with algebraic varieties and their generalizations (schemes, etc.)

Algebraic geometry is a branch of mathematics, classically studying 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.

Quotes

edit
  • While the move from dimension 2 to dimension 3 appears to be the obvious step there is a sense in which one should move from 2 to 4. This comes from the consideration of complex algebraic geometry. For complex dimension 1 this theory was started by Abel and continued by Riemann. For algebraic varieties of complex dimension n the real dimension is 2n, so the case n = 2 leads to 4-dimensional real manifolds. The key figures in the topology of higher-dimensional algebraic varieties were Lefschetz, Hodge, Cartan and Serre. While general algebraic geometry was one of the major developments of the second half of the 20th century, the topology of real 4-manifolds had a great surprise in store when Simon Donaldson made spectacular discoveries opening up an entirely new area.

See also

edit
edit
Wikipedia 
Wikipedia
Wikipedia has an article about:



Mathematics
Mathematicians
(by country)

AbelAnaxagorasArchimedesAristarchus of SamosAverroesArnoldBanachCantorCartanChernCohenDescartesDiophantusErdősEuclidEulerFourierGaussGödelGrassmannGrothendieckHamiltonHilbertHypatiaLagrangeLaplaceLeibnizMilnorNewtonvon NeumannNoetherPenrosePerelmanPoincaréPólyaPythagorasRiemannRussellSchwartzSerreTaoTarskiThalesTuringWeilWeylWilesWitten

Numbers

123360eπFibonacci numbersIrrational numberNegative numberNumberPrime numberQuaternionOctonion

Concepts

AbstractionAlgorithmsAxiomatic systemCompletenessDeductive reasoningDifferential equationDimensionEllipseElliptic curveExponential growthInfinityIntegrationGeodesicInductionProofPartial differential equationPrinciple of least actionPrisoner's dilemmaProbabilityRandomnessTheoremTopological spaceWave equation

Results

Euler's identityFermat's Last Theorem

Pure math

Abstract algebraAlgebraAnalysisAlgebraic geometry (Sheaf theory) • Algebraic topologyArithmeticCalculusCategory theoryCombinatoricsCommutative algebraComplex analysisDifferential calculusDifferential geometryDifferential topologyErgodic theoryFoundations of mathematicsFunctional analysisGame theoryGeometryGlobal analysisGraph theoryGroup theoryHarmonic analysisHomological algebraInvariant theoryLogicNon-Euclidean geometryNonstandard analysisNumber theoryNumerical analysisOperations researchRepresentation theoryRing theorySet theorySheaf theoryStatisticsSymplectic geometryTopology

Applied math

Computational fluid dynamicsEconometricsFluid mechanicsMathematical physicsScience

History of math

Ancient Greek mathematicsEuclid's ElementsHistory of algebraHistory of calculusHistory of logarithmsIndian mathematicsPrincipia Mathematica

Other

Mathematics and mysticismMathematics educationMathematics, from the points of view of the Mathematician and of the PhysicistPhilosophy of mathematicsUnification in science and mathematics