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

Abstract

We generalize Givental's Theorem for complete intersections in smooth toric varieties in the Fano case. In particular, we find Gromov--Witten invariants of Fano varieties of dimension $\ge 3$, which are complete intersections in weighted projective spaces and singular toric varieties. We generalize the Riemann-Roch equations to weighted projective spaces. We compute counting matrices of smooth Fano threefolds with Picard group Z and anticanonical degrees 2, 8, and 16.

16 pages, 1 figure, numerations in the journal and in the arxive differ

References in corpus (5)

• Relations between the correlators of the topological sigma-model coupled to gravity
• A mirror theorem for toric complete intersections
• Gromov-Witten invariants of Fano threefolds of genera 6 and 8
• New recursions for genus-zero Gromov-Witten invariants
• Absolute and relative Gromov-Witten invariants of very ample hypersurfaces

Cited by in corpus (1)

• Small toric degenerations of Fano threefolds