algebraic geometry
EnglishEdit
NounEdit
algebraic geometry (countable and uncountable, plural algebraic geometries)
 (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 ErrorCorrecting 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.
 1977, Robin Hartshorne, Algebraic Geometry, Springer, Softcover Reprint, 1977, page xiii,
Derived termsEdit
 derived algebraic geometry (= spectral algebraic geometry)
 differential algebraic geometry
 noncommutative algebraic geometry
 spectral algebraic geometry
Related termsEdit
TranslationsEdit
branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry


See alsoEdit
 analytic geometry
 differential geometry
 geometric algebra (mathematical structure)
 projective geometry
Further readingEdit
 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