2013/02/20 by Andrew Strangeway, Strangeway, Andrew
Mathematics · #14J45 (Secondary) #14N35 (Primary) #53D45 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J45 #msc:14N35 #msc:53D45
paper · pdf · doi:10.48550/arxiv.1302.5089
23 pages
arxiv created 2013/02/22 · arxiv updated 2013/02/25
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.