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arXiv · hep-th/9811124

On the Quantum Cohomology Rings of General Type Projective Hypersurfaces and Generalized Mirror Transformation

M. Jinzenji
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Abstract

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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M. Jinzenji. 1999-06-03. On the Quantum Cohomology Rings of General Type Projective Hypersurfaces and Generalized Mirror Transformation. https://doi.org/10.1142/s0217751x00000707

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