In algebraic geometry, the Kempf–Ness theorem, introduced by George Kempf and Linda Ness, gives a criterion for the stability of a vector in a representation of a complex reductive group. If the complex vector space is given a norm that is invariant under a maximal compact subgroup of the reductive group, then the Kempf–Ness theorem states that a vector is stable if and only if the norm attains a minimum value on the orbit of the vector.
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| - Kempf–Ness theorem (en)
- Kempf–Ness sats (sv)
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| - Inom matematiken är Kempf–Ness sats, introducerad av och Ness, kriterium för stabiliteten av en vektor i en av en komplex . Om det komplexa vektorrummet ges en norm som är under en av reduktiva gruppen, då säger Kempf–Ness sats att vektorn är stabil om och bara om normen når sitt minimivärde vid banan av vektorn. (sv)
- In algebraic geometry, the Kempf–Ness theorem, introduced by George Kempf and Linda Ness, gives a criterion for the stability of a vector in a representation of a complex reductive group. If the complex vector space is given a norm that is invariant under a maximal compact subgroup of the reductive group, then the Kempf–Ness theorem states that a vector is stable if and only if the norm attains a minimum value on the orbit of the vector. (en)
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| - In algebraic geometry, the Kempf–Ness theorem, introduced by George Kempf and Linda Ness, gives a criterion for the stability of a vector in a representation of a complex reductive group. If the complex vector space is given a norm that is invariant under a maximal compact subgroup of the reductive group, then the Kempf–Ness theorem states that a vector is stable if and only if the norm attains a minimum value on the orbit of the vector. The theorem has the following consequence: If X is a complex smooth projective variety and if G is a reductive complex Lie group, then (the GIT quotient of X by G) is homeomorphic to the symplectic quotient of X by a maximal compact subgroup of G. (en)
- Inom matematiken är Kempf–Ness sats, introducerad av och Ness, kriterium för stabiliteten av en vektor i en av en komplex . Om det komplexa vektorrummet ges en norm som är under en av reduktiva gruppen, då säger Kempf–Ness sats att vektorn är stabil om och bara om normen når sitt minimivärde vid banan av vektorn. (sv)
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