Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pfaffian Calabi-Yau threefolds, Stanley-Reisner schemes and mirror
  symmetry   Calabi-Yau manifolds are important objects in algebraic geometry and in
theoretical physics. A hypothesis of mirror symmetry is that Calabi-Yau
manifolds of dimension 3 come in pairs, with the Hodge numbers of one manifold
mirroring the Hodge numbers of the other.
  In this thesis, Calabi-Yau manifolds are constructed by smoothing
Stanley-Reisner schemes of triangulations of 3-spheres. The triangulations of
the 3-sphere with 7 or 8 vertices have been constructed and classified by
Gr\"unbaum and Sreedharan (1967). In this thesis we characterize the Calabi-Yau
manifolds obtained from the triangulations with 7 vertices. They are embedded
in six-dimensional projective space. Mirrors of such manifolds are constructed
by resolution of singularities performed on a singular fiber in the deformation
family of the Stanley-Reisner scheme. In this way, we reproduce the mirror by
R{\o}dland (1999) of a degree 14 pfaffian Calabi-Yau threefold, and the mirror
candidate by B\"ohm (2007) of a degree 13 pfaffian Calabi-Yau threefold. In the
latter case we verify that the Hodge numbers in fact constitute a mirror, using
toric geometry.

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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th