eBook ISBN:  9781470438005 
Product Code:  AMSIP/9.E 
List Price:  $67.00 
MAA Member Price:  $60.30 
AMS Member Price:  $53.60 
eBook ISBN:  9781470438005 
Product Code:  AMSIP/9.E 
List Price:  $67.00 
MAA Member Price:  $60.30 
AMS Member Price:  $53.60 

Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 9; 1998; 444 ppMSC: Primary 14; Secondary 32; 81
This volume is an updated edition of Essays on Mirror Manifolds, the first book of papers published after the phenomenon of mirror symmetry was discovered. The two major groups who made the discovery reported their papers here.
Greene, Plesser, and Candelas gave details on their findings; Witten gave his interpretation which was vital for future development. Vafa introduced the concept of quantum cohomology. Several mathematicians, including Katz, Morrison, Wilson, Roan, Tian, Hübsch, Yau, and Borcea discussed current knowledge about CalabiYau manifolds. Ferrara and his coauthors addressed special geometry and \(N=2\) supergravity. Roček proposed possible mirrors for CalabiYau manifolds with torsion. This collection continues to be an important book on this spectacular achievement in algebraic geometry and mathematical physics.
Also available from the AMS are the related volumes, Mirror Symmetry II (1996), Mirror Symmetry III (1999), and Mirror Symmetry IV (2002).
Titles in this series are copublished with International Press of Boston, Inc., Cambridge, MA.
ReadershipGraduate students, research mathematicians and mathematical physicists working in algebraic geometry, mathematical physics, and number theory.

Table of Contents

Chapters

An introduction to mirror manifolds

A pair of CalabiYau manifolds as an exactly soluble superconformal theory

Topological mirrors and quantum rings

Mirror manifolds and topological field theory

Rational curves and classification of algebraic varieties

Rational curves on CalabiYau threefolds

PicardFuchs equations and mirror maps for hypersurfaces

Kähler classes on CalabiYau threefolds—An informal survey

Automorphic functions and special Kähler geometry

PicardFuchs equations and flat holomorphic connections from $N = 2$ supergravity

A new geometry from superstring theory

The geometry of CalabiYau orbifolds

Properties of superstring vacua from (topological) LandauGinzburg models

An $SL(2,\mathbb {C})$ action on certain Jacobian rings and the mirror map

A generalized construction of mirror manifolds

New constructions of mirror manifolds: Probing moduli space far from Fermat points

Deformations of CalabiYau Kleinfolds

Smoothing 3folds with trivial canonical bundle and ordinary double points

Modified CalabiYau manifolds with torsion

CalabiYau threefolds and complex multiplication


Reviews

From a review of the first edition ...
This volume is very timely, giving very broad coverage of one of the important developments in mathematics and physics today ... This volume is a requisite for those working in the area of CY \(3\)folds, as well as those interested in mathematical implications of contemporary physics.
Mathematical Reviews


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This volume is an updated edition of Essays on Mirror Manifolds, the first book of papers published after the phenomenon of mirror symmetry was discovered. The two major groups who made the discovery reported their papers here.
Greene, Plesser, and Candelas gave details on their findings; Witten gave his interpretation which was vital for future development. Vafa introduced the concept of quantum cohomology. Several mathematicians, including Katz, Morrison, Wilson, Roan, Tian, Hübsch, Yau, and Borcea discussed current knowledge about CalabiYau manifolds. Ferrara and his coauthors addressed special geometry and \(N=2\) supergravity. Roček proposed possible mirrors for CalabiYau manifolds with torsion. This collection continues to be an important book on this spectacular achievement in algebraic geometry and mathematical physics.
Also available from the AMS are the related volumes, Mirror Symmetry II (1996), Mirror Symmetry III (1999), and Mirror Symmetry IV (2002).
Titles in this series are copublished with International Press of Boston, Inc., Cambridge, MA.
Graduate students, research mathematicians and mathematical physicists working in algebraic geometry, mathematical physics, and number theory.

Chapters

An introduction to mirror manifolds

A pair of CalabiYau manifolds as an exactly soluble superconformal theory

Topological mirrors and quantum rings

Mirror manifolds and topological field theory

Rational curves and classification of algebraic varieties

Rational curves on CalabiYau threefolds

PicardFuchs equations and mirror maps for hypersurfaces

Kähler classes on CalabiYau threefolds—An informal survey

Automorphic functions and special Kähler geometry

PicardFuchs equations and flat holomorphic connections from $N = 2$ supergravity

A new geometry from superstring theory

The geometry of CalabiYau orbifolds

Properties of superstring vacua from (topological) LandauGinzburg models

An $SL(2,\mathbb {C})$ action on certain Jacobian rings and the mirror map

A generalized construction of mirror manifolds

New constructions of mirror manifolds: Probing moduli space far from Fermat points

Deformations of CalabiYau Kleinfolds

Smoothing 3folds with trivial canonical bundle and ordinary double points

Modified CalabiYau manifolds with torsion

CalabiYau threefolds and complex multiplication

From a review of the first edition ...
This volume is very timely, giving very broad coverage of one of the important developments in mathematics and physics today ... This volume is a requisite for those working in the area of CY \(3\)folds, as well as those interested in mathematical implications of contemporary physics.
Mathematical Reviews