We study ACM bundles on cubic fourfolds containing a plane exploiting the geometry of the associated quadric fibration and Kuznetsov’s treatment of their bounded derived categories of coherent sheaves. More precisely, we recover the K3 surface naturally associated to the fourfold as a moduli space of Gieseker stable ACM bundles of rank four.
Arithmetically Cohen-Macaulay bundles on cubic fourfolds containing a plane / M. Lahoz, E. Macrì, P. Stellari (PROGRESS IN MATHEMATICS). - In: Brauer groups and obstruction problems : moduli spaces and arithmetic / [a cura di] A. Auel, B. Hassett, A. Várilly-Alvarado, B. Viray. - Cham : Birkhäuser, 2017. - ISBN 9783319468518. - pp. 155-175 [10.1007/978-3-319-46852-5_8]
Arithmetically Cohen-Macaulay bundles on cubic fourfolds containing a plane
P. Stellari
2017
Abstract
We study ACM bundles on cubic fourfolds containing a plane exploiting the geometry of the associated quadric fibration and Kuznetsov’s treatment of their bounded derived categories of coherent sheaves. More precisely, we recover the K3 surface naturally associated to the fourfold as a moduli space of Gieseker stable ACM bundles of rank four.
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