#
*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.

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.

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

mirror symmetry
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.

You can contact the authors at the following email addresses:

dacox@amherst.edu
katz@math.uiuc.edu