Concept information
Preferred term
algebraic geometry
Definition(s)
-
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. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of points of special interest like singular points, inflection points and points at infinity. More advanced questions involve the topology of the curve and the relationship between curves defined by different equations.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Algebraic_geometry)
Broader concept(s)
Narrower concept(s)
- algebraic K-theory
- algebraic variety
- birational geometry
- cotangent complex
- deformation
- derived algebraic geometry
- Diophantine geometry
- enumerative geometry
- generalized flag variety
- generalized Riemann hypothesis
- Gröbner basis
- Gromov-Witten invariant
- Hitchin integrable system
- homotopy associative algebra
- inversive geometry
- Jacobi elliptic function
- LLT polynomial
- Macdonald polynomial
- moduli space
- moment problem
- motivic cohomology
- noncommutative geometry
- ordered field
- period
- residue field
- Riemann-Roch theorem
- Schottky problem
- sheaf
- tensor field
- tropical geometry
- Whitney umbrella
- Zariski tangent space
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-SKGJ9CKK-N
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