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 in the sense of Gentili-Struppa, 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 / Gentili, Graziano; Gori, Anna; Sarfatti, Giulia. - In: JOURNAL OF SYMPLECTIC GEOMETRY. - ISSN 1527-5256. - STAMPA. - 17:(2019), pp. 267-300. [10.4310/JSG.2019.v17.n1.a7]
Quaternionic toric manifolds
SARFATTI, GIULIA
2019-01-01
Abstract
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 in the sense of Gentili-Struppa, 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
