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Quantum reconstruction for Fano bundles on projective space

Published online by Cambridge University Press:  11 January 2016

Andrew Strangeway*
Affiliation:
Department of Mathematics, Imperial College London, London, SW7 2AZ, United [email protected]
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Abstract

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We present a reconstruction theorem for Fano vector bundles on projective space which recovers the small quantum cohomology for the projectivization 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 program.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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