On Quantum Cohomology Rings for Hypersurfaces in $CP^{N-1}$

Details On Quantum Cohomology Rings for Hypersurfaces in $CP^{N-1}$ On Quantum Cohomology Rings for Hypersurfaces in $CP^{N-1}$

1995-11-29

arxiv.org/abs/hep-th/9511206v2

J.Math.Phys. 38 (1997) 6613-6638

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, Revised version

Scientific paper

10.1063/1.532228

Using the torus action method, we construct one variable polynomial representation of quantum cohomology ring for degree $k$ hypersurface in $CP^{N-1}$ . The results interpolate the well-known result of $CP^{N-2}$ model and the one of Calabi-Yau hypersuface in $CP^{N-1}$. We find in $k\leq N-2$ case, principal relation of this ring have very simple form compatible with toric compactification of moduli space of holomorphic maps from $CP^{1}$ to $CP^{N-1}$.

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