Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\partial\bar{\partial}$-complex symplectic and Calabi-Yau manifolds:
  Albanese map, deformations and period maps   Let $X$ be a compact complex manifold with trivial canonical bundle and
satisfying the $\partial\bar{\partial}$-Lemma. We show that the Kuranishi space
of $X$ is a smooth universal deformation and that small deformations enjoy the
same properties as $X$. If, in addition, $X$ admits a complex symplectic form,
then the local Torelli theorem holds and we obtain some information about the
period map.
  We clarify the structure of such manifolds a little by showing that the
Albanese map is a surjective submersion.

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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs