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Torus invariant transverse Kähler foliations


Author: Hiroaki Ishida
Journal: Trans. Amer. Math. Soc. 369 (2017), 5137-5155
MSC (2010): Primary 53D20; Secondary 14M25, 32M05, 57S25
DOI: https://doi.org/10.1090/tran/7070
Published electronically: March 17, 2017
MathSciNet review: 3632563
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Abstract: In this paper, we show the convexity of the image of a moment map on a transverse symplectic manifold equipped with a torus action under a certain condition. We also study properties of moment maps in the case of transverse Kähler manifolds. As an application, we give a positive answer to the conjecture posed by Cupit-Foutou and Zaffran.


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Additional Information

Hiroaki Ishida
Affiliation: Department of Mathematics and Computer Science, Graduate School of Science and Engineering, Kagoshima University, Korimoto 1-21-40, Kagoshima 890-0065, Japan
Email: ishida@sci.kagoshima-u.ac.jp

DOI: https://doi.org/10.1090/tran/7070
Keywords: Torus action, complex manifold, toric variety, moment-angle manifold, LVM manifold, LVMB manifold, non-K\"ahler manifold, transverse K\"ahler form, moment map
Received by editor(s): October 12, 2015
Received by editor(s) in revised form: May 17, 2016
Published electronically: March 17, 2017
Additional Notes: The author was supported by JSPS Research Fellowships for Young Scientists
Article copyright: © Copyright 2017 American Mathematical Society