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arXiv · 1108.4766

Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces

Masao Jinzenji·Masahide Shimizu
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Abstract

In this paper, we generalize Walcher's computation of the open Gromov-Witten invariants of the quintic hypersurface to Fano and Calabi-Yau projective hypersurfaces. Our main tool is the open virtual structure constants. We also propose the generalized mirror transformation for the open Gromov-Witten invariants, some parts of which are proven explicitly. We also discuss possible modification of the multiple covering formula for the case of higher dimensional Calabi-Yau manifolds. The generalized disk invariants for some Calabi-Yau and Fano manifolds are shown and they are certainly integers after re-summation by the modified multiple covering formula. This paper also contains the direct integration method of the period integrals for higher dimensional Calabi-Yau hypersurfaces in the appendix.

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Masao Jinzenji, Masahide Shimizu. 2011-08-24. Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces. https://doi.org/10.1142/s0219887814500054

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