Mirror symmetry began when theoretical physicists made some
astonishing predictions about rational curves on quintic
hypersurfaces in four-dimensional projective space. Understanding
the mathematics behind these predictions has been a substantial
challenge. This work a comprehensive monographs on mirror symmetry,
covering the original observations by the physicists through to
progress made. Subjects discussed include: toric varieties Hodge
theory Kahler geometry moduli of stable maps Calabi-Yau manifolds
quantum cohomology Gromov-Witten invariants and the mirror theorem.
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