Convexity for Hamiltonian torus actions on \(b\)-symplectic manifolds
type: Item
instance of: scholarly article
title: Convexity for Hamiltonian torus actions on \(b\)-symplectic manifolds
zbMATH Open document ID: 1390.53094
author: Eva Miranda
author: Ana Rita Pires
author: Geoffrey Scott
author: Victor Guillemin
published in: Mathematical Research Letters
publication date: 2018-03-29T00:00:00Z
review text: This paper follows earlier work by the authors, where the Delzant theorem was generalised to \(b\)-symplectic manifolds (also known as log-symplectic). Recall that the Delzant theorem states that symplectic toric manifolds can be recovered from the image of the associated moment map. The convexity of this image is the key property on which the proof of the theorem is based. In this article the authors consider a \(b\)-symplectic manifold of dimension \(2n\), whose singular locus contains compact leaves. This manifold may be acted by a torus of dimension smaller than \(n\). Using results from [the authors et al., Int. Math. Res. Not. 2015, No. 14, 5818--5848 (2015; Zbl 1333.53115)] and following the classical proof of \textit{M. F. Atiyah} [Bull. Lond. Math. Soc. 14, 1--15 (1982; Zbl 0482.58013)], they show that the image of the moment map is convex. The modular weights associated with the exceptional hypersurface play an important role in the proof.
reviewed by: Iakovos Androulidakis
Mathematics Subject Classification ID: 53D20
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 57S15
zbMATH DE Number: 6854507
zbMATH Keywords: \(b\)-symplectic manifold
zbMATH Keywords: Hamiltonian toric action
zbMATH Keywords: convexity
zbMATH Keywords: log-symplectic
MaRDI profile type: Publication
full work available at URL: mrl.2017.v24.n2.a5
OpenAlex ID: W2963617329
DOI: 10.4310/MRL.2017.V24.N2.A5
description: scientific article; zbMATH DE number 6854507