We compute the quantum cohomology ring Hφ∗(P,C) of
an arbitrary d-dimensional smooth projective toric manifold PΣ associated with a fan Σ. The multiplicative structure of
Hφ∗(PΣ,C) depends on the choice of an element
avarphi in the ordinary cohomology group H2(PΣ,C).
There are many properties of the quantum cohomology rings Hφ∗(PΣ,C) which are supposed to be valid for quantum cohomology
rings of K\"ahler manifoldsComment: 23 pages, Late