Mathematicians wanting to get into the field ... will find a very well written and encyclopaedic account of the mathematics which was needed in, and was developed from, what now might be termed classical mirror symmetry. —Bulletin of the LMS The book is highly recommended for everyone who wants to learn about the fascinating recent interplay between physics and mathematics. —Mathematical Reviews 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 a 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, Kahler geometry, moduli of stable maps, Calabi-Yau manifolds, quantum cohomology, Gromov-Witten invariants, and the mirror theorem.
This introduction to the algebro-geometric aspects of mirror symmetry used by physicists is primarily for mathematicians interested in the field. It begins with the quintic threefold, toric geometry, and mirror constructions. The next chapters on Yukawa couplings, moduli spaces, Gromov-Witten invariants, and quantum cohomology flesh out the mathematics needed to formulate a precise version of mirror symmetry. Localization and quantum differential equations are then reviewed before presenting recent proofs of the Mirror Theorem. An appendix summarizes key points of physical theories mentioned in the book. Annotation c. by Book News, Inc., Portland, Or.
Book Details
Published
September 28, 1999
Publisher
Providence, R.I. : American Mathematical Society, c1999.
