Mirror symmetry and quantum cohomology of projective bundles

Details Mirror symmetry and quantum cohomology of projective bundles Mirror symmetry and quantum cohomology of projective bundles

2006-10-25

arxiv.org/abs/math/0610758v1

Mathematics

Algebraic Geometry

9 pages

Scientific paper

In an earlier paper we conjectured a relation between the quantum $\mathcal D$-modules of a smooth variety $X$ and the projectivisation of a direct sum of line bundles over it. In this paper we prove the conjecture when $X$ is a complete intersection in a toric variety. We also use the conjecture to show that the relations of the small quantum cohomology ring of $X$ that come from differential operators lift to the projective bundle. The basic cohomology relation of the projective bundle deforms to a relation in the small quantum cohomology.

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