On the Quantum Cohomology Rings of General Type Projective Hypersurfaces and Generalized Mirror Transformation
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 CalabiYau 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 threepoint GromovWitten 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.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 2000
 DOI:
 10.1142/S0217751X00000707
 arXiv:
 arXiv:hepth/9811124
 Bibcode:
 2000IJMPA..15.1557J
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 32 pages, 3 figures, discussion in section 5 is refined, some minor errors are corrected