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We report interesting examples of Calabi-Yau threefolds where birational geometry and geometry of Fourier-Mukai partners of a Calabi-Yau manifold arise naturally from studying its mirror family of Calabi-Yau manifolds.We define mirror symmetry in terms of families of Calabi-Yau manifolds in general. We will find for our examples that all expected geometry of Calabi-Yau manifolds arises from special boundary points, called LCSL points, in the parameter space of mirror Calabi-Yau manifolds.

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Mirror symmetry from families of Calabi-Yau manifolds

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  • 发表日期：

    2026年

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  • Shinobu Hosono,
  • Hiromichi Takagi

摘要

We report interesting examples of Calabi-Yau threefolds where birational geometry and geometry of Fourier-Mukai partners of a Calabi-Yau manifold arise naturally from studying its mirror family of Calabi-Yau manifolds.We define mirror symmetry in terms of families of Calabi-Yau manifolds in general. We will find for our examples that all expected geometry of Calabi-Yau manifolds arises from special boundary points, called LCSL points, in the parameter space of mirror Calabi-Yau manifolds.