| eBook ISBN: | 978-1-4704-3800-5 |
| Product Code: | AMSIP/9.E |
| List Price: | $67.00 |
| MAA Member Price: | $60.30 |
| AMS Member Price: | $53.60 |
| eBook ISBN: | 978-1-4704-3800-5 |
| Product Code: | AMSIP/9.E |
| List Price: | $67.00 |
| MAA Member Price: | $60.30 |
| AMS Member Price: | $53.60 |
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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 Calabi-Yau manifolds. Ferrara and his coauthors addressed special geometry and \(N=2\) supergravity. Roček proposed possible mirrors for Calabi-Yau 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 co-published with International Press of Boston, Inc., Cambridge, MA.
ReadershipGraduate students, research mathematicians and mathematical physicists working in algebraic geometry, mathematical physics, and number theory.
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Table of Contents
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Chapters
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An introduction to mirror manifolds
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A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
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Topological mirrors and quantum rings
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Mirror manifolds and topological field theory
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Rational curves and classification of algebraic varieties
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Rational curves on Calabi-Yau threefolds
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Picard-Fuchs equations and mirror maps for hypersurfaces
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Kähler classes on Calabi-Yau threefolds—An informal survey
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Automorphic functions and special Kähler geometry
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Picard-Fuchs equations and flat holomorphic connections from $N = 2$ supergravity
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A new geometry from superstring theory
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The geometry of Calabi-Yau orbifolds
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Properties of superstring vacua from (topological) Landau-Ginzburg models
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An $SL(2,\mathbb {C})$ action on certain Jacobian rings and the mirror map
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A generalized construction of mirror manifolds
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New constructions of mirror manifolds: Probing moduli space far from Fermat points
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Deformations of Calabi-Yau Kleinfolds
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Smoothing 3-folds with trivial canonical bundle and ordinary double points
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Modified Calabi-Yau manifolds with torsion
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Calabi-Yau threefolds and complex multiplication
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Reviews
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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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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
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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 Calabi-Yau manifolds. Ferrara and his coauthors addressed special geometry and \(N=2\) supergravity. Roček proposed possible mirrors for Calabi-Yau 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 co-published 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 Calabi-Yau 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 Calabi-Yau threefolds
-
Picard-Fuchs equations and mirror maps for hypersurfaces
-
Kähler classes on Calabi-Yau threefolds—An informal survey
-
Automorphic functions and special Kähler geometry
-
Picard-Fuchs equations and flat holomorphic connections from $N = 2$ supergravity
-
A new geometry from superstring theory
-
The geometry of Calabi-Yau orbifolds
-
Properties of superstring vacua from (topological) Landau-Ginzburg 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 Calabi-Yau Kleinfolds
-
Smoothing 3-folds with trivial canonical bundle and ordinary double points
-
Modified Calabi-Yau manifolds with torsion
-
Calabi-Yau 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
