Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformations of Noncompact Calabi-Yau threefolds   We describe deformations of the noncompact Calabi-Yau threefolds $W_k =
\mbox{Tot}(\mathcal{O}_{\mathbb{P}^1}(-k) \oplus
\mathcal{O}_{\mathbb{P}^1}(k-2))$ for $k=1,2,3$, as well as their moduli of
holomorphic vector bundles of rank $2$. Deformations are computed concretely by
calculations of $H^1(W_k, TW_k)$. Information about the moduli of vector
bundles is obtained by analysing bundles that are extensions of line bundles.
We show that for each $k=1,2,3$ the associated structures are qualitatively
different, and we also comment on their difference from the analogous
structures for the simpler noncompact twofolds
$\mbox{Tot}(\mathcal{O}_{\mathbb{P}^1}(-k))$ which had been studied previously
by the authors.
  We describe deformations of the noncompact Calabi-Yau threefolds $W_k =
\textrm{Tot}(\mathcal{O}_{\mathbb{P}^1}(-k) \oplus
\mathcal{O}_{\mathbb{P}^1}(k-2))$ for $k=1,2,3$. We compute deformations
concretely by calculations of $\textrm{H}^1(W_k, TW_k)$ via \v{C}ech
cohomology. We show that for each $k=1,2,3$ the associated structures are
qualitatively different, and we also comment on their difference from the
analogous structures of simpler noncompact twofolds
$\textrm{Tot}(\mathcal{O}_{\mathbb{P}^1}(-k))$.

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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph