Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Short Tops and Semistable Degenerations   One may construct a large class of Calabi-Yau varieties by taking
anticanonical hypersurfaces in toric varieties obtained from reflexive
polytopes. If the intersection of a reflexive polytope with a hyperplane
through the origin yields a lower-dimensional reflexive polytope, then the
corresponding Calabi-Yau varieties are fibered by lower-dimensional Calabi-Yau
varieties. A top generalizes the idea of splitting a reflexive polytope into
two pieces. In contrast to the classification of reflexive polytopes, there are
infinite families of equivalence classes of tops. Tops may be used to describe
either fibrations or degenerations of Calabi-Yau varieties. We give a simple
combinatorial condition on tops which produces semistable degenerations of K3
surfaces, and, when appropriate smoothness conditions are met, semistable
degenerations of Calabi-Yau threefolds. Our method is constructive: given a
fixed reflexive polytope which will lie on the boundary of the top, we describe
an algorithm for constructing tops which yields semistable degenerations of the
corresponding hypersurfaces. The properties of each degeneration may be
computed directly from the combinatorial structure of the top.

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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cs