We hope that this volume is a natural sequel to mirror symmetry, 242, written by hori, katz, klemm, pandharipande, thomas, vafa, vakil and zaslow, which was a product of the. Period and mirrormaps for the quartic k3 springerlink. Introduction despite being the focus of a great deal of attention, kontsevichs homo. In this paper, we introduce the interested reader to homological mirror symmetry. The idea is that along with the equality h1,1x h2,1y of moduli numbers of kahler structures on x and of. This book furnishes a brief introduction to classical mirror symmetry, a term. Current interest to mirror manifolds is due to the so called mirror conjecture and its. Homological mirror symmetry is a mathematical conjecture made by maxim kontsevich. In this paper we will make a bridge between two approaches. The present volume, intended to be a monograph, covers mirror symmetry from the homological and torus. Mirror symmetry comes from statements in supersymmetric string theory.
Mathematically mirror symmetry can be interpreted in many ways. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory. In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called calabiyau manifolds. Homological mirror symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years.
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