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OPEN VIRTUAL STRUCTURE CONSTANTS AND MIRROR COMPUTATION OF OPEN GROMOV–WITTEN INVARIANTS OF PROJECTIVE HYPERSURFACES

MASAO JINZENJI

Department of Mathematics, Graduate School of Science, Hokkaido University, Kita-ku, Sapporo 060-0810, Japan

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and

MASAHIDE SHIMIZU

Institute for the Advancement of Higher Education, Hokkaido University, Kita-ku, Sapporo 060-0817, Japan

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https://doi.org/10.1142/S0219887814500054Cited by:2 (Source: Crossref)

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 resummation 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.

Keywords:

AMSC: 14N35, 14J32, 14J33

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