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

GAUSS–MANIN SYSTEM AND THE VIRTUAL STRUCTURE CONSTANTS