algebraic geometry

English

Noun

algebraic geometry (countable and uncountable, plural algebraic geometries)

1. (mathematics) 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.
   • 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.

   • 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.

   • 2013, Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen, William Traves, An Invitation to Algebraic Geometry, Springer, page 1:

     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.

Derived terms

• derived algebraic geometry (= spectral algebraic geometry)
• differential algebraic geometry
• noncommutative algebraic geometry
• spectral algebraic geometry

Related terms

• algebrogeometric

Translations

branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry

• Armenian: հանրահաշվական երկրաչափություն (hanrahašvakan erkračʻapʻutʻyun)
• Chinese:

  Mandarin: 代數幾何／代数几何 (zh) (dàishù jǐhé)

• Czech: algebraická geometrie f
• Danish: algebraisk geometri c
• Finnish: algebrallinen geometria
• French: géométrie algébrique (fr) f
• Galician: xeometría alxebraica f
• German: algebraische Geometrie f
• Hungarian: algebrai geometria (hu)
• Italian: geometria algebrica (it) f
• Japanese: 代数幾何学 (だいすうきかがく, daisū kikagaku)
• Macedonian: алгебарска геометрија f (algebarska geometrija)
• Portuguese: geometria algébrica f
• Russian: алгебраи́ческая геоме́трия f (algebraíčeskaja geométrija)
• Spanish: geometría algebraica f
• Swedish: algebraisk geometri (sv) c

See also

• analytic geometry
• differential geometry
• geometric algebra (mathematical structure)
• projective geometry

Further reading

• Glossary of algebraic geometry on Wikipedia.Wikipedia
• Glossary of classical algebraic geometry on Wikipedia.Wikipedia
• Derived algebraic geometry on Wikipedia.Wikipedia
• Differential geometry on Wikipedia.Wikipedia
  • Differential algebraic geometry on Wikipedia.Wikipedia
• Intersection theory on Wikipedia.Wikipedia
• Noncommutative algebraic geometry on Wikipedia.Wikipedia
• Real algebraic geometry on Wikipedia.Wikipedia