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Examples of non-Kaehler Hamiltonian torus actions

Susan Tolman
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Abstract

An important question with a rich history is the extent to which the symplectic category is larger than the Kaehler category. Many interesting examples of non-Kaehler symplectic manifolds have been constructed. However, sufficiently large symmetries can force a symplectic manifold to be Kaehler. In this paper, we solve several outstanding problems by constructing the first symplectic manifold with large non-trivial symmetries which does not admit an invariant Kaehler structure. The proof that it is not Kaehler is based on the Atiyah-Guillemin-Sternberg convexity theorem. Using the ideas of this paper, C. Woodward shows that even the symplectic analogue of spherical varieties need not be Kaehler.

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BibTeXRIS

Susan Tolman. 1995-11-16. Examples of non-Kaehler Hamiltonian torus actions. https://arxiv.org/abs/dg-ga/9511007

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