Remarks on the abelian convexity theorem

Leonardo Biliotti; Alessandro Ghigi

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arXiv · 1801.01778

Remarks on the abelian convexity theorem

Leonardo Biliotti·Alessandro Ghigi

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Abstract

This note 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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Leonardo Biliotti, Alessandro Ghigi. 2018-01-05. Remarks on the abelian convexity theorem. https://arxiv.org/abs/1801.01778

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