New Series: SMF/AMS Texts & Monographs,  Vol. 1 
 

Voisin, V.:

 Mirror Symmetry 

			

The first chapter is devoted to the geometry of Clabi-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, of 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 fIat cnnection 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.



Sep. 1999 			120 pp.



0-8218-1947-X 				4,940



 A. M. S.



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