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; 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.

Mirror Symmetry (Smf/Ams Texts and Monographs, V. 1)

Science & Math

Claire Voisin

Mathematics

American Mathemataical Society

The Herons of Europe (Poyser Monographs)

A C Black Publishers Ltd

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Books by Claire Voisin

See the best price to sell, buy, or rent books by Claire Voisin. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Mirror Symmetry (Smf/Ams Texts and Monographs, V. 1)

The Herons of Europe (Poyser Monographs)