Quantum Cohomology Rings of Toric Manifolds

Details Quantum Cohomology Rings of Toric Manifolds Quantum Cohomology Rings of Toric Manifolds

1993-10-05

arxiv.org/abs/alg-geom/9310004v2

Mathematics

Algebraic Geometry

23 pages, Latex

Scientific paper

We compute the quantum cohomology ring $H^*_{\varphi}({\bf P}, {\bf C})$ of an arbitrary $d$-dimensional smooth projective toric manifold ${\bf P}_{\Sigma}$ associated with a fan $\Sigma$. The multiplicative structure of $H^*_{\varphi}({\bf P}_{\Sigma}, {\bf C})$ depends on the choice of an element $avarphi$ in the ordinary cohomology group $H^2({\bf P}_{\Sigma}, {\bf C})$. There are many properties of the quantum cohomology rings $H^*_{\varphi}({\bf P}_{\Sigma}, {\bf C})$ which are supposed to be valid for quantum cohomology rings of K\"ahler manifolds

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