Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Aspects of Mirror Symmetry (with SYZ for Rigid CY manifolds)   In this article we discuss the geometry of moduli spaces of (1) flat bundles
over special Lagrangian submanifolds and (2) deformed Hermitian-Yang-Mills
bundles over complex submanifolds in Calabi-Yau manifolds.
  These moduli spaces reflect the geometry of the Calabi-Yau itself like a
mirror. Strominger, Yau and Zaslow conjecture that the mirror Calabi-Yau
manifold is such a moduli space and they argue that the mirror symmetry duality
is a Fourier-Mukai transformation. We review various aspects of the mirror
symmetry conjecture and discuss a geometric approach in proving it.
  The existence of rigid Calabi-Yau manifolds poses a serious challenge to the
conjecture. The proposed mirror partners for them are higher dimensional
generalized Calabi-Yau manifolds. For example, the mirror partner for a certain
K3 surface is a cubic fourfold and its Fano variety of lines is birational to
the Hilbert scheme of two points on the K3. This hyperkahler manifold can be
interpreted as the SYZ mirror of the K3 by considering singular special
Lagrangian tori.
  We also compare the geometries between a CY and its associated generalized
CY. In particular we present a new construction of Lagrangian submanifolds.

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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin