Mirror Symmetry (Smf/Ams Texts and Monographs, V. 1) by Claire Voisin (PDF)

Description

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.

User’s Reviews

Editorial Reviews: From the Publisher Without any doubt, the English version of this panoramic introduction to the phenomenon of mirror symmetry will find a much larger number of interesting readers than the Frech original could do, and that is what this beautiful text really deserves. Zentralblatt f”ur Mathematik”

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a concise introduction to mirror symmetry, and it is very useful reference to read about Hodge theory aspects of mirror symmetry.

⭐If you know the difficulty of the content, then wait no more and buy this book. Prof Voisin is définitive in hodge theory.If you think of a real mirror then this book is not for you.

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