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 book is the first completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, Kähler geometry, moduli of stable maps, Calabi-Yau manifolds, quantum cohomology, Gromov-Witten invariants, and the mirror theorem.

Features:

• Numerous examples worked out in detail
• An appendix on mathematical physics
• An exposition of the algebraic theory of Gromov-Witten invariants and quantum cohomology
• A proof of the mirror theorem for the quintic threefold

Readership

Graduate students, research mathematicians interested in the relations between mathematics and physics; algebraic geometers, symplectic geometers, and theoretical physicists.