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A mathematical proof of a formula of Aspinwall and Morrison. (English) Zbl 0951.14025

Summary: We give a rigorous proof of the Aspinwall-Morrison formula [cf. P. S. Aspinwall and D. R. Morrison, Commun. Math. Phys. 151, No. 2, 245-262 (1993; Zbl 0776.53043)] which expresses the cubic derivatives of the Gromov-Witten as a series depending only on the number of rational curves in each homology class, for a Calabi-Yau threefold with only rigid immersed rational curves.

MSC:

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14J30 \(3\)-folds

Citations:

Zbl 0776.53043
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References:

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