Corpus ID: 16958948

Quantum Cohomology Rings of Toric Manifolds

  title={Quantum Cohomology Rings of Toric Manifolds},
  author={V. Batyrev},
  journal={arXiv: Algebraic Geometry},
  • V. Batyrev
  • Published 1993
  • Mathematics
  • arXiv: Algebraic Geometry
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… Expand
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