Remarks on the abelian convexity theorem

Biliotti, Leonardo; Ghigi, Alessandro

doi:10.1090/proc/14188

Remarks on the abelian convexity theorem
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Proc. Amer. Math. Soc. 146 (2018), 5409-5419 Request permission

Abstract:

This paper contains some observations on abelian convexity theorems. 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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