About: Algebraic geometry and analytic geometry

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In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. The deep relation between these subjects has numerous applications in which algebraic techniques are applied to analytic spaces and analytic techniques to algebraic varieties.

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rdfs:label	Algebraic geometry and analytic geometry (en) 가가 정리 (ko) 代数幾何学と解析幾何学 (ja) 代數幾何與解析幾何 (zh)
rdfs:comment	In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. The deep relation between these subjects has numerous applications in which algebraic techniques are applied to analytic spaces and analytic techniques to algebraic varieties. (en) 대수기하학에서 가가 정리(GAGA定理, 영어: GAGA theorems)는 복소수에 대한 사영 스킴이 해석적 다양체와 유사한 성질을 갖는다는 것을 보이는 일련의 정리들이다. (ko) 数学において、代数幾何学と解析幾何学（フランス語: Géometrie Algébrique et Géométrie Analytique、略称: GAGA）は密接な関係にある。代数幾何学は代数多様体を研究するのに対して、解析幾何学は複素多様体やより一般的に多変数の（複素）解析函数のゼロ点で局所的に定義されたを扱う。これら2つの深い関係は、代数的なテクニックを解析空間へ適用したり、逆に解析的テクニックを代数多様体へ適用したりする上で応用されている。 (ja) 在數學中，代數幾何與解析幾何是兩個關係密切的學科。代數幾何研究代數簇，在複數域上，同時也能以複分析及微分幾何的技術研究代數簇。讓-皮埃爾·塞爾在1956年的同名論文中比較了這兩種觀點。在 SGA 第一冊附錄中，則以概形論的語言重新表述。 (zh)
dcterms:subject	Analytic geometry Algebraic geometry
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Link from a Wikipage to another Wikipage	Projective space Meromorphic function Algebraically closed field Annales de l'Institut Fourier Holomorphic function Riemann surface Compact space Complex analytic space Holomorphic function Analytic space Mathematical logic Mathematics Liouville's theorem (complex analysis) Complex manifold Function field of an algebraic variety Fundamental group Permutation representation Wei-Liang Chow Coherent sheaves Alexander Grothendieck Alfred Tarski Algebraic curve Algebraic geometry Algebraic variety Analytic geometry Finite extension Kodaira vanishing theorem Jean-Pierre Serre Riemann sphere Algebraic geometry Characteristic (algebra) Hodge theory Solomon Lefschetz Ramification (mathematics) Complex coordinate space Sheaf (mathematics) Oka coherence theorem Zariski topology Space (mathematics) BY-NC-SA Strong topology Springer-Verlag Laurent expansion Complex projective line Structure sheaf dbr:Amnon_Neeman
Link from a Wikipage to an external page	https://ocw.mit.edu/courses/mathematics/18-726-algebraic-geometry-spring-2009/lecture-notes https://www.college-de-france.fr/media/jean-pierre-serre/UPL5435398796951750634_Serre_FAC.pdf https://www.math.upenn.edu/~harbater/patch35.pdf%7Curl= https://ocw.mit.edu/courses/mathematics/18-726-algebraic-geometry-spring-2009/lecture-notes/MIT18_726s09_lec22_gaga.pdf https://link.springer.com/chapter/10.1007%2FBFb0058667%7Cdoi=10.1007/BFb0058656%7Clanguage=fr http://www.numdam.org/numdam-bin/item%3Fid=AIF_1956__6__1_0 http://gdz.sub.uni-goettingen.de/dms/resolveppn/%3FPPN=GDZPPN002286920
sameAs	Algebraic geometry and analytic geometry Algebraic geometry and analytic geometry Algebraic geometry and analytic geometry Algebraic geometry and analytic geometry Algebraic geometry and analytic geometry Algebraic geometry and analytic geometry
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has abstract	In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. The deep relation between these subjects has numerous applications in which algebraic techniques are applied to analytic spaces and analytic techniques to algebraic varieties. (en) 대수기하학에서 가가 정리(GAGA定理, 영어: GAGA theorems)는 복소수에 대한 사영 스킴이 해석적 다양체와 유사한 성질을 갖는다는 것을 보이는 일련의 정리들이다. (ko) 数学において、代数幾何学と解析幾何学（フランス語: Géometrie Algébrique et Géométrie Analytique、略称: GAGA）は密接な関係にある。代数幾何学は代数多様体を研究するのに対して、解析幾何学は複素多様体やより一般的に多変数の（複素）解析函数のゼロ点で局所的に定義されたを扱う。これら2つの深い関係は、代数的なテクニックを解析空間へ適用したり、逆に解析的テクニックを代数多様体へ適用したりする上で応用されている。 (ja) 在數學中，代數幾何與解析幾何是兩個關係密切的學科。代數幾何研究代數簇，在複數域上，同時也能以複分析及微分幾何的技術研究代數簇。讓-皮埃爾·塞爾在1956年的同名論文中比較了這兩種觀點。在 SGA 第一冊附錄中，則以概形論的語言重新表述。 (zh)
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foaf:isPrimaryTopicOf	wikipedia-en:Algebraic_geometry_and_analytic_geometry
is Link from a Wikipage to another Wikipage of	List of algebraic geometry topics Beryl May Dent Algebraic manifold Hodge conjecture Riemann surface Gaga (disambiguation) List of important publications in mathematics Timeline of category theory and related mathematics Complexification (Lie group) Function of several complex variables

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