This paper contains some observations on abelian convexity the- orems. Convexity along an orbit is established in a very general setting using Kempf–Ness functions. This is applied to give short proofs of the Atiyah– Guillemin–Sternberg theorem and of abelian convexity for the gradient map in the case of a real analytic submanifold of complex projective space. Finally we give an application to the action on the probability measures.

Remarks on the Abelian convexity theorem

Ghigi A.
2018-01-01

Abstract

This paper contains some observations on abelian convexity the- orems. Convexity along an orbit is established in a very general setting using Kempf–Ness functions. This is applied to give short proofs of the Atiyah– Guillemin–Sternberg theorem and of abelian convexity for the gradient map in the case of a real analytic submanifold of complex projective space. Finally we give an application to the action on the probability measures.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1287228
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