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
rdfs:label	Geometric invariant theory (en)
rdfs:comment	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	Fixed-point subgroup
sameAs	Geometric invariant theory Geometric invariant theory
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:ISBN dbt:Main dbt:Math dbt:Redirect-distinguish dbt:MathSciNet
Subject	Algebraic groups Scheme theory Invariant theory Moduli theory
gold:hypernym	Method
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Geometric_invariant_theory?oldid=1074178789&ns=0
Wikipage page ID	1639003 (xsd:integer)
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Wikipage revision ID	1074178789 (xsd:integer)
Link from a Wikipage to another Wikipage	Francesco Severi Group (mathematics) Locally finite collection Projective linear group Projective space William Haboush Abstract algebra Affine variety Alexander Grothendieck Algebra over a field Algebraic curve Algebraic geometry Algebraic variety Bernhard Riemann Birational geometry Monopole (mathematics) Vladimir Popov (mathematician) Bridgeland stability condition Categorical quotient Algebraic groups Scheme theory General linear group Genus (mathematics) Geometric complexity theory Geometric quotient Glossary of algebraic geometry Glossary of topology Invariant theory David Hilbert David Mumford Differential geometry Hilbert scheme Hilbert–Mumford criterion Quantization commutes with reduction Chow variety Classical group K-stability K-stability of Fano varieties Publications Mathématiques de l'IHÉS Springer Science+Business Media Codimension Compact space Compactification (mathematics) Connected space Hilbert's fourteenth problem Morphism of algebraic varieties Equivalence relation Equivariant topology Ernest Vinberg Function field of an algebraic variety GIT quotient Morphism of schemes Symplectic geometry Group action Haboush's theorem Hausdorff space Instanton Invariant (mathematics) David Hilbert Moduli scheme Moduli space Vector space Stable curve Stable vector bundle Masayoshi Nagata Mathematics Quotient space (topology) Algebraic fraction Reductive group Representable functor Representation theory Riemann surface Ring of polynomial functions Singular point of an algebraic variety Moduli theory dbr:Polarization_of_an_algebraic_variety
has abstract	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. Geometric invariant theory studies an action of a group G on an algebraic variety (or scheme) X and provides techniques for forming the 'quotient' of X by G as a scheme with reasonable properties. One motivation was to construct moduli spaces in algebraic geometry as quotients of schemes parametrizing marked objects. In the 1970s and 1980s the theory developed interactions with symplectic geometry and equivariant topology, and was used to construct moduli spaces of objects in differential geometry, such as instantons and monopoles. (en)

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