Kempf–Ness theorem

Kempf–Ness theorem In algebraic geometry, the Kempf–Ness theorem, introduced by George Kempf and Linda Ness (1979), 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, alors {displaystyle X/!/g} (the GIT quotient of X by G) is homeomorphic to the symplectic quotient of X by a maximal compact subgroup of G.

References Kempf, George; Ness, Linda (1979), "The length of vectors in representation spaces", Géométrie algébrique (Proc. Summer Meeting, Université. Copenhagen, Copenhagen, 1978), Notes de cours en mathématiques, volume. 732, Berlin, New York: Springer Verlag, pp. 233–243, est ce que je:10.1007/BFb0066647, ISBN 978-3-540-09527-9, M 0555701 This algebraic geometry–related article is a stub. Vous pouvez aider Wikipédia en l'agrandissant.

Catégories: Invariant theoryTheorems in algebraic geometryAlgebraic geometry stubs

Si vous voulez connaître d'autres articles similaires à Kempf–Ness theorem vous pouvez visiter la catégorie Stubs de géométrie algébrique.

Laisser un commentaire

Votre adresse email ne sera pas publiée.


Nous utilisons nos propres cookies et ceux de tiers pour améliorer l'expérience utilisateur Plus d'informations