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arXiv · 1612.03600

Quaternionic toric manifolds

Graziano Gentili·Anna Gori·Giulia Sarfatti
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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 ${\rm Sp}(1)$ 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.

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BibTeXRIS

Graziano Gentili, Anna Gori, Giulia Sarfatti. 2016-12-12. Quaternionic toric manifolds. https://arxiv.org/abs/1612.03600

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