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

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

2005-07-12

arxiv.org/abs/math/0507232v3

Mathematics

Algebraic Geometry

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

Scientific paper

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 $\geq 3$, 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.

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