On the Structure of Small Quantum Cohomology Rings for Projective Hypersurfaces

We prove the fact that correlation functions of topological sigma model (A-model) on Fano hypersurfaces in $CP^{N-1}$ can be written as polynomials of correlation functions of degree 1 (number of lines, or Schubert numbers) up to degree 3. We extend the above formalism to the case of Calabi-Yau hypersurface in $CP^{N-1}$ and explain the above characteristic is conserved in the case of Calabi-Yau hypersurfaces (up to degree 3). We also obtained numerically satisfying results for degree 4 rational curves. Our formalism has close relation to the hypergeometric series used in the mirror calculation