About: Complex geometry

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In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis.

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rdfs:label	هندسة عقدية (ar) Kompleksa geometrio (eo) Complex geometry (en) Géométrie complexe (fr) Geometri kompleks (in) Geometria complessa (it) 複素幾何学 (ja) Complexe meetkunde (nl) Geometria complexa (pt)
rdfs:comment	الهندسة العقدية هي تطبيق الأعداد العقدية على الهندسة المستوية. بدلا من تمثيل نقطة في مستو بزوج من الإحداثيات الديكارتية، يمكن تمثيلها بعدد مركب وحيد، يمكن كتابته بالشكل المستطيل أو القطبي . (ar) In matematica, e in particolare in geometria, per geometria complessa si intende lo studio delle varietà complesse, di dimensione arbitraria. Le varietà complesse sono generalmente studiate con metodi algebrici o analitici. La geometria complessa è quindi un'area avente una forte sovrapposizione con la geometria algebrica, la geometria differenziale e l'analisi complessa (quest'ultima soprattutto per quanto riguarda lo studio delle varietà di dimensione 1, le cosiddette superfici di Riemann). (it) La géométrie complexe est un pan entier de la géométrie, intéressé dans l'étude des ouverts de l'espace vectoriel complexe Cn, et par extension des variétés holomorphes. (fr) 数学では、複素幾何学（ふくそきかがく、complex geometry）は複素多様体や多変数複素函数の研究をする。複素解析における幾何学的な側面であるは代数幾何学への超越な応用は、この分野に属する。本記事を通して、「解析的」という用語は簡単のために省略することがある。例えば、部分多様体や超曲面は、「解析的」という形容詞は省略する。また、他の記事の使いかたに従い、多様体(variety)は既約(irreducible)であることを仮定する。 (ja) In de complexe analyse en de algebraïsche meetkunde, deelgebieden van de wiskunde, is de complexe meetkunde de studie van complexe variëteiten en functies van meer complexe variabelen. Toepassing van transcendentale methoden in de algebraïsche meetkunde valt in deze categorie, net als de meer meetkundige hoofdstukken van de complexe analyse. (nl) Em matemática, a geometria complexa é o estudo das variedades complexas e das funções de várias . A área inclui a aplicação de métodos transcendentais à geometria algébrica, juntamente com aspectos mais geométricos da análise complexa. (pt) En matematiko, kompleksa geometrio estas la apliko de kompleksaj nombroj al ebena geometrio. Anstataŭ ol prezenti punkton en la ebeno kiel paro de karteziaj koordinatoj, oni povas esti prezenti ĝin kiel unu kompleksan nombron, kiu povas esti skribita laŭvole en ortangula aŭ trigonometria prezento. Kompleksa analitika geometrio konsideras solvadon de geometriaj problemoj, aparte tiuj kiuj engaĝas angulojn, per kompleksa algebro. Uzante eŭleran formulon eblas prezenti ĉiun rotacion kiel kompleksa nombro. (eo) In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis. (en) Dalam matematika, geometri kompleks adalah studi tentang , , dan fungsi . Penerapan metode transendental ke geometri aljabar termasuk dalam kategori ini, bersama dengan lebih banyak aspek geometris analisis kompleks. (in)
foaf:depiction
dcterms:subject	Complex manifolds Several complex variables Algebraic geometry
Wikipage page ID	186101 (xsd:integer)
Wikipage revision ID	1118841078 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Cartan's theorems A and B Quaternion Enriques–Kodaira classification Enumerative geometry List of complex and algebraic surfaces Representation theory Toric varieties Bernhard Riemann Borel–Weil–Bott theorem Ddbar lemma Deformation theory Almost complex manifold Complex manifolds Hodge conjecture Holomorphic function Holomorphic vector bundle Homeomorphic Hyperkähler manifold Atiyah-Singer index theorem Ricci curvature Jacobian variety Elliptic curves Kähler–Einstein metric John Wiley & Sons Pseudoconvexity Compact space Complex analysis Complex analytic space Complex number Complex plane Complex polytope Analysis Several complex variables Mathematics Gauge theory Gauge theory (mathematics) Elliptic curve Elsevier Fubini-Study metric GAGA Geometry Mirror symmetry (string theory) Möbius transformation Conformal field theory Constant scalar curvature Kähler metric SYZ conjecture Holomorphic vector bundles Homogeneous polynomials Orthant Liouville's theorem (complex analysis) Analytic variety Calabi conjecture Calabi–Yau manifold Singularity (mathematics) String theory Complex Lie group Complex algebraic variety

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