Beschreibung:
This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov-Witten invariants of a Calabi-Yau threefold by using the Picard-Fuchs differential equation of period integrals of its mirror Calabi-Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold.
Restricts readers' attention to the best-known example of mirror symmetry: a quintic hypersurface in CP^4
1. Brief Introduction of Mirror Symmetry.- 2. Topological Sigma Models (A-Model and B-Model).- 3. Basics of Geometry of Complex Manifolds.- 4. Detailed Computation of B-Model Prediction.- 5. Moduli space of Holomorphic Maps from CP^1 to CP^{N-1}.- 6. Localization Computation.- 7. Brief Outline of Direct Proof of Mirror Theorem.