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

Givental's theorem for complete intersections in smooth toric varieties is generalized to Fano varieties. The Gromov-Witten invariants are found for Fano varieties of dimension >= 3 that are complete intersections in weighted projective spaces or singular toric varieties. A generalized Riemann-Roch equation is also obtained for such varieties. As a consequence, the counting matrices of smooth Fano threefolds with Picard group Z and anticanonical degrees 2, 8, and 16 are calculated.