Abstract
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 and anticanonical degrees 2, 8, and 16 are calculated.Bibliography: 29 titles.
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