On Mirror Symmetry Conjecture for Schoen's Calabi-Yau 3 folds

Shinobu Hosono; Masa-Hiko Saito; Jan Stienstra

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On Mirror Symmetry Conjecture for Schoen's Calabi-Yau 3 folds

Shinobu Hosono·Masa-Hiko Saito·Jan Stienstra

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Abstract

In this paper, we verify a part of the Mirror Symmetry Conjecture for Schoen's Calabi-Yau 3-fold, which is a special complete intersection in a toric variety. We calculate a part of the prepotential of the A-model Yukawa couplings of the Calabi-Yau 3-fold directly by means of a theta function and Dedekind's eta function. This gives infinitely many Gromov-Witten invariants, and equivalently infinitely many sets of rational curves in the Calabi-Yau 3-fold. Using the toric mirror construction, we also calculate the prepotential of the B-model Yukawa couplings of the mirror partner. Comparing the expansion of the B-model prepotential with that of the A-model prepotential, we check a part of the Mirror Symmetry Conjecture up to a high order.

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Shinobu Hosono, Masa-Hiko Saito, Jan Stienstra. 1997-09-25. On Mirror Symmetry Conjecture for Schoen's Calabi-Yau 3 folds. https://arxiv.org/abs/alg-geom/9709027

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