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Rational curves on hypersurfaces [after A. Givental]. (English) Zbl 0932.14029
Séminaire Bourbaki. Volume 1997/98. Exposés 835–849. Paris: Société Mathématique de France, Astérisque. 252, 307-340, Exp. No. 848 (1998).
The paper is a description (from the algebro-geometric point of view) of the relationship between hypergeometric series and the quantum cohomology of hypersurfaces in projective space, which the remarkable work done by A. B. Givental [Int. Math. Res. Not. 1996, No. 13, 613–663 (1996; Zbl 0881.55006)] has unveiled.
A particular case of this relationship is Givental’s proof of the prediction about the number of rational curves on the Calabi-Yau quintic 3-fold made by Candelas, de la Ossa, Green and Parkes.
For the entire collection see [Zbl 0911.00019].

MSC:
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
14J70 Hypersurfaces and algebraic geometry
14H10 Families, moduli of curves (algebraic)
14H81 Relationships between algebraic curves and physics
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14J30 \(3\)-folds
14J45 Fano varieties
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