A Reconstruction Theorem for Quantum Cohomology of Fano Bundles on Projective Space

Andrew Strangeway

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arXiv · 1302.5089

A Reconstruction Theorem for Quantum Cohomology of Fano Bundles on Projective Space

Andrew Strangeway

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Abstract

We present a reconstruction theorem for Fano vector bundles on projective space which recovers the small quantum cohomology for the projectivisation of the bundle from a small number of low-degree Gromov--Witten invariants. We provide an extended example in which we calculate the quantum cohomology of a certain Fano 9-fold and deduce from this, using the quantum Lefschetz theorem, the quantum period sequence for a Fano 3-fold of Picard rank 2 and degree 24. This example is new, and is important for the Fanosearch programme.

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Andrew Strangeway. 2013-02-20. A Reconstruction Theorem for Quantum Cohomology of Fano Bundles on Projective Space. https://arxiv.org/abs/1302.5089

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