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We generalize Givental's Theorem for complete intersections in smooth toricvarieties in the Fano case. In particular, we find Gromov--Witten invariants ofFano varieties of dimension $\geq 3$, which are complete intersections inweighted projective spaces and singular toric varieties. We generalize theRiemann-Roch equations to weighted projective spaces. We compute countingmatrices of smooth Fano threefolds with Picard group Z and anticanonicaldegrees 2, 8, and 16.

Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties