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

V. V. Przyjalkowski

Sbornik. Mathematics, Tome 198 (2007) no. 9, pp. 1325-1340

Résumé

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 $\geqslant3$ 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 $\mathbb Z$ and anticanonical degrees 2, 8, and 16 are calculated. Bibliography: 29 titles.

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