Gauss-Manin system and the virtual structure constants

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11 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)445-477
Number of pages33
JournalInternational Journal of Mathematics
Issue number5
Publication statusPublished - Jul 2002
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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