In the present paper we introduce and study a new notion of toric manifold in the quaternionic setting. We develop a construction with which, starting from appropriate m-dimensional Delzant polytopes, we obtain manifolds of real dimension 4m, acted on by m copies of the group Sp(1) of unit quaternions. These manifolds are quaternionic regular and can be endowed with a 4-plectic structure and a generalized moment map. Convexity properties of the image of the moment map are studied. Quaternionic toric manifolds appear to be a large enough class of examples where one can test and study new results in quaternionic geometry.
Quaternionic Toric Manifolds / G. Gentili, A. Gori, G. Sarfatti. - In: JOURNAL OF SYMPLECTIC GEOMETRY. - ISSN 1527-5256. - 17:1(2019), pp. 267-301.
Titolo: | Quaternionic Toric Manifolds |
Autori: | |
Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria |
Progetto: | Real and Complex Manifolds: Geometry, Topology and Harmonic Analysis |
Data di pubblicazione: | 2019 |
Rivista: | |
Tipologia: | Article (author) |
Data ahead of print / Data di stampa: | 2018 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.4310/JSG.2019.v17.n1.a7 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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File | Descrizione | Tipologia | Licenza | |
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toricJSG.pdf | Toric quaternionic manifolds | Post-print, accepted manuscript ecc. (versione accettata dall'editore) | Open Access Visualizza/Apri |