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Mirror Symmetry

Mirror Symmetry

Buch | Softcover
120 Seiten
1999
American Mathematical Society (Verlag)
978-0-8218-1947-0 (ISBN)
CHF 52,25 inkl. MwSt
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An English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The book focuses on the geometry of Calabi-Yau manifolds, and describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry.
This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry.The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; and, the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the Calabi-Yau case. The book concludes with the first 'naive' Givental computation, which is a mysterious mathematical justification of the computation of Candelas, et al.

Calabi-Yau manifolds "Physical" origin of the conjecture The work of Candelas-de la Ossa-Green-Parkes The work of Batyrev Quantum cohomology The Givental construction Bibliography.

Erscheint lt. Verlag 1.1.2000
Reihe/Serie SMF/AMS Texts & Monographs
Verlagsort Providence
Sprache englisch
Gewicht 269 g
Themenwelt Mathematik / Informatik Mathematik Geometrie / Topologie
Mathematik / Informatik Mathematik Graphentheorie
Naturwissenschaften Physik / Astronomie Quantenphysik
ISBN-10 0-8218-1947-X / 082181947X
ISBN-13 978-0-8218-1947-0 / 9780821819470
Zustand Neuware
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