Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Remarks on the abelian convexity theorem


Authors: Leonardo Biliotti and Alessandro Ghigi
Journal: Proc. Amer. Math. Soc. 146 (2018), 5409-5419
MSC (2010): Primary 53D20; Secondary 32M05, 14L24
DOI: https://doi.org/10.1090/proc/14188
Published electronically: September 17, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53D20, 32M05, 14L24

Retrieve articles in all journals with MSC (2010): 53D20, 32M05, 14L24


Additional Information

Leonardo Biliotti
Affiliation: Department of Mathematics, Università degli Studi di Parma, via Università, 12-I 43121 Parma, Italy
Email: leonardo.biliotti@unipr.it

Alessandro Ghigi
Affiliation: Department of Mathematics, Università degli Studi di Pavia, via Università, 12-I 43121 Parma, Italy
Email: alessandro.ghigi@unipv.it

DOI: https://doi.org/10.1090/proc/14188
Keywords: K\"ahler manifolds, moment maps, geometric invariant theory, probability measures.
Received by editor(s): January 5, 2018
Received by editor(s) in revised form: March 30, 2018, and April 5, 2018
Published electronically: September 17, 2018
Additional Notes: The authors were partially supported by FIRB 2012 “Geometria differenziale e teoria geometrica delle funzioni” and by GNSAGA of INdAM. The first author was also supported by MIUR PRIN 2015 “Real and Complex Manifolds: Geometry, Topology and Harmonic Analysis”. The second author was also supported by MIUR PRIN 2015 “Moduli spaces and Lie theory”.
Communicated by: Michael Wolf
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society