Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A compact symmetric symplectic non-Kaehler manifold   In this paper I construct, using off the shelf components, a compact
symplectic manifold with a non-trivial Hamiltonian circle action that admits no
Kaehler structure. The non-triviality of the action is guaranteed by the
existence of an isolated fixed point.
  The motivation for this work comes from the program of classification of
Hamiltonian group actions. The Audin-Ahara-Hattori-Karshon classification of
Hamiltonian circle actions on compact symplectic 4-manifolds showed that all of
such manifolds are Kaehler. Delzant's classification of $2n$-dimensional
symplectic manifolds with Hamiltonian action of $n$-dimensional tori showed
that all such manifolds are projective toric varieties, hence Kaehler. An
example in this paper show that not all compact symplectic manifolds that admit
Hamiltonian torus actions are Kaehler. Similar technique allows us to construct
a compact symplectic manifold with a Hamiltonian circle action that admits no
invariant complex structures, no invariant polarizations, etc.

35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin