Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Primitive Calabi-Yau Threefolds   A primitive Calabi-Yau threefold is a non-singular Calabi-Yau threefold which
cannot be written as a crepant resolution of a singular fibre of a degeneration
of Calabi-Yau threefolds. These should be thought as the most basic Calabi-Yau
manifolds; all others should arise through degenerations of these. This paper
first continues the study of smoothability of Calabi-Yau threefolds with
canonical singularities begun in the author's previous paper, ``Deforming
Calabi-Yau Threefolds.'' (alg-geom 9506022). If X' is a non-singular Calabi-Yau
threefold, and f:X'->X is a contraction of a divisor to a curve, we obtain
results on when X is smoothable. We then discuss applications of this result to
the classification of primitive Calabi-Yau threefolds. Combining the
deformation theoretic results of this paper with those of ``Deforming
Calabi-Yau Threefolds,'' we obtain strong restrictions on the class of
primitive Calabi-Yau threefolds. We also speculate on how such work might yield
results on connecting together all moduli spaces of Calabi-Yau threefolds.

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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph