ON THE QUANTUM COHOMOLOGY RINGS OF GENERAL TYPE PROJECTIVE HYPERSURFACES AND GENERALIZED MIRROR TRANSFORMATION

MASAO JINZENJI
2000 International Journal of Modern Physics A  
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
more » ... 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.
doi:10.1142/s0217751x00000707 fatcat:afe7yqckv5brpdx7gsvbild4by