Dictionary

algebraic geometry en · NOUN

Meanings

1. (countable, uncountable) A branch of mathematics that studies algebraic varieties (solution sets of polynomial equations) and their generalisations, using techniques from both algebra (chiefly commutative algebra) and geometry.
   • For example, every high school mathematics student has studied a bit of algebraic geometry, in learning the basic properties of conic sections, such as parabolas and hyperbolas. 2013, Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, William Traves, An Invitation to Algebraic Geometry, Springer, page 1:
   • 2003, Ian F. Blake, Curves with Many Points and Their Applications, Marc Fossorier, Hideki Imai, Shu Lin, Alain Poli (editors), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, Proceedings, Springer, LNCS 1719, page 55, The use of curves in algebraic geometries, in applications such as coding and cryptography, now has an extensive literature and has been responsible for dramatic developments in both subjects.
   • 1977, Robin Hartshorne, Algebraic Geometry, Springer, Softcover Reprint, 1977, page xiii, The author of an introductory book on algebraic geometry has the difficult task of providing geometrical insight and examples, while at the same time developing the modern technical language of the subject. For in algebraic geometry, a great gap appears to separate the intuitive ideas which form the point of departure from the technical methods used in modern research. The first question is that of language. Algebraic geometry has developed in waves, each with its own language and point of view.

Forms

Deriveds

differential algebraic geometry · spectral algebraic geometry · noncommutative algebraic geometry · derived algebraic geometry

Relateds

algebrogeometric · differential geometry · projective geometry · geometric algebra · analytic geometry

Translations (17)

ja 代数幾何学 (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · pl geometria algebraiczna (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · fi algebrallinen geometria (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · gl xeometría alxebraica (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · da algebraisk geometri (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · cs algebraická geometrie (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · pt geometria algébrica (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · it geometria algebrica (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · hu algebrai geometria (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · mk алгебарска геометрија (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · sv algebraisk geometri (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · hy հանրահաշվական երկրաչափություն (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · cmn 代數幾何 /代数几何 (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · ru алгебраи́ческая геоме́трия (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · de algebraische Geometrie (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · fr géométrie algébrique (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry) · es geometría algebraica (branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry)