Mathematics – Algebraic Geometry
Scientific paper
1997-09-25
Mathematics
Algebraic Geometry
LaTeX Version 2.09, 36 pages. Submitted to The Proceedings of Taniguchi Symposium 1997, "Integrable Systems and Algebraic Geom
Scientific paper
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.
Hosono Shinobu
Saito Masa-Hiko
Stienstra Jan
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