Virtual Gromov-Witten Invariants and the Quantum Cohomology Rings of General Type Projective Hypersurfaces

Details Virtual Gromov-Witten Invariants and the Quantum Cohomology Rings of General Type Projective Hypersurfaces Virtual Gromov-Witten Invariants and the Quantum Cohomology Rings of General Type Projective Hypersurfaces

2000-02-12

arxiv.org/abs/math/0002095v2

Mod.Phys.Lett. A15 (2000) 629-650

Mathematics

Algebraic Geometry

16 pages, Latex, some comments added, minor errors are corrected

Scientific paper

10.1142/S0217732300000633

In this paper, we propose another characterization of the generalized mirror transformation on the quantum cohomology rings of general type projective hypersurfaces. This characterics is useful for explicit determination of the form of the generalized mirror transformation. As applications, we rederive the generalized mirror transformation up to $d=3$ rational Gromov-Witten invariants obtained in our previous article, and determine explicitly the the generalized mirror transformation for the $d=4, 5$ rational Gromov-Witten invariants in the case when the first Chern class of the hypersurface equals $-H$ (i.e., $k-N=1$).

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