Mirror symmetry from families of Calabi-Yau manifolds

Abstract: 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.