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Quantum reconstruction for Fano bundles on projective space

Part of: Projective and enumerative geometry Surfaces and higher-dimensional varieties Symplectic geometry, contact geometry

Published online by Cambridge University Press:  11 January 2016

Andrew Strangeway
Andrew Strangeway*
Affiliation:
Department of Mathematics, Imperial College London, London, SW7 2AZ, United Kingdoma.strangeway09@imperial.ac.uk
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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.

MSC classification

Secondary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds 14J45: Fano varieties
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 218 , June 2015 , pp. 1 - 28
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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