About: Stability (algebraic geometry)

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In mathematics, and especially algebraic geometry, stability is a notion which characterises when a geometric object, for example a point, an algebraic variety, a vector bundle, or a sheaf, has some desirable properties for the purpose of classifying them. The exact characterisation of what it means to be stable depends on the type of geometric object, but all such examples share the property of having a minimal amount of internal symmetry, that is such stable objects have few automorphisms. This is related to the concept of simplicity in mathematics, which measures when some mathematical object has few subobjects inside it (see for example simple groups, which have no non-trivial normal subgroups). In addition to stability, some objects may be described with terms such as semi-stable (hav

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rdfs:label	Stability (algebraic geometry) (en)
rdfs:comment	In mathematics, and especially algebraic geometry, stability is a notion which characterises when a geometric object, for example a point, an algebraic variety, a vector bundle, or a sheaf, has some desirable properties for the purpose of classifying them. The exact characterisation of what it means to be stable depends on the type of geometric object, but all such examples share the property of having a minimal amount of internal symmetry, that is such stable objects have few automorphisms. This is related to the concept of simplicity in mathematics, which measures when some mathematical object has few subobjects inside it (see for example simple groups, which have no non-trivial normal subgroups). In addition to stability, some objects may be described with terms such as semi-stable (hav (en)
foaf:depiction
dcterms:subject	Algebraic geometry
Wikipage page ID	64246583 (xsd:integer)
Wikipage revision ID	1119036998 (xsd:integer)
Link from a Wikipage to another Wikipage	Calculus of variations Bernhard Riemann David Hilbert David Mumford Kähler–Einstein metric Mathematical beauty Mathematics Geometric analysis Simple group Functional (mathematics) Geometric invariant theory Geometry Singularity (mathematics) Point (geometry) Symmetry (geometry) Automorphism GIT quotient K-stability Algebraic geometry Algebraic variety Partial differential equations Kempf–Ness theorem Kobayashi–Hitchin correspondence Quotient space Invariant theory Algebraic geometry Moduli of algebraic curves Moduli space Differential geometry Categorical quotient Yang–Mills equations Yau–Tian–Donaldson conjecture Sheaf (mathematics) Slope stability Uniformization theorem Vector bundle Moment map Nonabelian Hodge correspondence Gieseker stability Symplectic quotient Bridgeland stability
sameAs	Stability (algebraic geometry) Stability (algebraic geometry)
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has abstract	In mathematics, and especially algebraic geometry, stability is a notion which characterises when a geometric object, for example a point, an algebraic variety, a vector bundle, or a sheaf, has some desirable properties for the purpose of classifying them. The exact characterisation of what it means to be stable depends on the type of geometric object, but all such examples share the property of having a minimal amount of internal symmetry, that is such stable objects have few automorphisms. This is related to the concept of simplicity in mathematics, which measures when some mathematical object has few subobjects inside it (see for example simple groups, which have no non-trivial normal subgroups). In addition to stability, some objects may be described with terms such as semi-stable (having a small but not minimal amount of symmetry), polystable (being made out of stable objects), or unstable (having too much symmetry, the opposite of stable). (en)
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is Link from a Wikipage to another Wikipage of	Geometric invariant theory Stability
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is foaf:primaryTopic of	wikipedia-en:Stability_(algebraic_geometry)

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