Quantum Cohomology Rings of Toric Manifolds
Abstract
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 Kähler manifolds
- Publication:
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arXiv e-prints
- Pub Date:
- October 1993
- DOI:
- 10.48550/arXiv.alg-geom/9310004
- arXiv:
- arXiv:alg-geom/9310004
- Bibcode:
- 1993alg.geom.10004B
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- 23 pages, Latex