Gauss-Manin System and the Virtual Structure Constants

Details Gauss-Manin System and the Virtual Structure Constants Gauss-Manin System and the Virtual Structure Constants

2001-09-06

arxiv.org/abs/math/0109039v2

Int.J.Math. 13 (2002) 445-478

Mathematics

Algebraic Geometry

25 pages, Latex, references added, minor errors are corrected

Scientific paper

In this paper, we discuss some applications of Givental's differential equations to enumerative problems on rational curves in projective hypersurfaces. Using this method, we prove some of the conjectures on the structure constants of quantum cohomology of projective hypersurfaces, proposed in our previous article. Moreover, we clarify the correspondence between the virtual structure constants and Givental's differential equations when the projective hypersurface is Calabi-Yau or general type.

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