Mirror Symmetry and Algebraic Geometry
Mathematical Surveys and Monographs
Volume 68
American Mathematical Society, 1999

by

David A. Cox,
Amherst College
Sheldon Katz,
University of Illinois at Urbana-Champaign

What's in the Book

This monograph is an introduction to the mathematics of mirror symmetry, with a special emphasis on its algebro-geometric aspects. Topics covered include the quintic threefold, toric geometry, Hodge theory, complex and Kähler moduli, Gromov-Witten invariants, quantum cohomology, localization in equivariant cohomology, and the recent work of Lian-Liu-Yau and Givental on the Mirror Theorem. The book is written for algebraic geometers and graduate students who want to learn about mirror symmetry. It is also a reference for specialists in the field and background reading for physicists who want to see the mathematical underpinnings of the subject.

Typographical Errors

A list of typographical errors is available for the first printing of Mirror Symmetry and Algebraic Geometry: TeX source or postscript .

Also, Proposition 5.5.4 on page 98 is incorrect and the proof given on pages 99 and 100 has some gaps. The above list of typographical errors gives the correct statement of the proposition but is not able to fix all of the errors in the proof (the correct proof is a much longer argument which doesn't fit into the space available on page 99). If you want to see the full details of the proof, click here for a postscript file of the proof.

Contacting the American Mathematical Society

To find Mirror Symmetry and Algebraic Geometry in the AMS on-line catalog, go to the AMS bookstore and enter

in the Quick Search. This brings up a list of all AMS publications which touch on mirror symmetry (there are a lot). From here, it is easy to get to the catalog entry for our book, which includes a brief description and ordering information.

Contacting the Authors

You can contact the authors at the following email addresses: