Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-11-13
Int.J.Mod.Phys. A15 (2000) 1557-1596
Physics
High Energy Physics
High Energy Physics - Theory
32 pages, 3 figures, discussion in section 5 is refined, some minor errors are corrected
Scientific paper
10.1142/S0217751X00000707
In this paper, we study the structure of the quantum cohomology ring of a projective hypersurface with non-positive 1st 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 a good correspondence with the terms that appear in the generalized mirror transformation.
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