On the quantum cohomology rings of general type projective hypersurfaces and generalized mirror transformation

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9 Citations (Scopus)

Abstract

In this paper, we study the structure of the quantum cohomology ring of a projective hypersurface with nonpositive first Chern class. We prove a theorem which suggests that the mirror transformation of the quantum cohomology of a projective Calabi-Yau hypersurface has a close relation with the ring of symmetric functions, or with Schur polynomials. With this result in mind, we propose a generalized mirror transformation on the quantum cohomology of a hypersurface with negative first Chern class and construct an explicit prediction formula for three-point Gromov-Witten invariants up to cubic rational curves. We also construct a projective space resolution of the moduli space of polynomial maps, which is in good correspondence with the terms that appear in the generalized mirror transformation.

Original languageEnglish
Pages (from-to)1557-1595
Number of pages39
JournalInternational Journal of Modern Physics A
Volume15
Issue number11
DOIs
Publication statusPublished - Apr 30 2000
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics
  • Astronomy and Astrophysics

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