About: Geometric invariant theory

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In mathematics, geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces. It was developed by David Mumford in 1965, using ideas from the paper in classical invariant theory.

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rdf:type	Thing software yago:Abstraction100002137 yago:Group100031264 yago:WikicatAlgebraicGroups
rdfs:label	Geometric invariant theory (en) 안정점 (ko) 幾何学的不変式論 (ja)
rdfs:comment	대수기하학에서, 안정점(安定點, 영어: stable point)은 어떤 대수군의, 사영 대수다양체 위의 작용 아래, 그 안정자군이 유한하며, 그 궤도가 닫힌집합인 점이다. (ko) 数学では、幾何学的不変式論(Geometric invariant theory)（もしくは、GIT）は、代数幾何学でモジュライ空間の構成に使用する目的で、群作用による商を構成する方法である。幾何学的不変論は、デヴィッド・マンフォード(David Mumford)により、1965年、古典的(invariant theory)での論文のアイデアを使って開発された。幾何学的不変式論は、代数多様体（もしくは、スキーム）上の群 G による群作用を研究し、合理的な性質を持つスキームとして G による X の「商」を構成するテクニックをもたらす。動機の一つは、代数幾何学でのモジュライ空間を、マークされた対象をパラメトライズするスキームの商として構成することにあった。1970年代と1980年代には、シンプレクティック幾何学や(equivariant topology)と相互作用しながら発展し、(instanton)や(monopoles)のような微分幾何学での対象のモジュライ空間の構成に使われた。 (ja) In mathematics, geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces. It was developed by David Mumford in 1965, using ideas from the paper in classical invariant theory. (en)
differentFrom	Stable fixed point
dcterms:subject	Moduli theory Algebraic groups Invariant theory Scheme theory
Wikipage page ID	1639003 (xsd:integer)
Wikipage revision ID	1119366114 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective space Monopole (mathematics) Representation theory Non-singular David Hilbert David Mumford Algebra over a field Moduli theory Riemann Riemann surface Vector space Instanton Invariant (mathematics) Algebraic groups Compact space Masayoshi Nagata Mathematics General linear group Geometric complexity theory Geometric quotient Classical group Invariant theory Connected space Equivariant topology Stable vector bundle Compactification (mathematics) Function field of an algebraic variety Stability (algebraic geometry) Publications Mathématiques de l'IHÉS GIT quotient Haboush's theorem Hausdorff space K-stability K-stability of Fano varieties Ring of polynomial functions Algebraic curve Algebraic geometry Algebraic variety Equivalence relation Ernest Vinberg Francesco Severi Bridgeland stability condition Hilbert's fourteenth problem Hilbert–Mumford criterion William Haboush Quotient space (topology) Rational function Regular function Group (mathematics) Group action (mathematics) Hilbert scheme Invariant theory Quantization commutes with reduction Abstract algebra Birational geometry Symplectic geometry Codimension Moduli space Reductive group Differential geometry Scheme theory Scheme theory Orbit (group theory) Categorical quotient Scheme (mathematics) Locally closed Stable curve Representable functor Vladimir L. Popov Affine algebraic variety Springer-Verlag Orbit space G-invariant Chow scheme Classical Lie group Grothendieck Quotient topology Quotient variety Projective group Genus (curve) Geometric point Coarse moduli problem

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