Data di Pubblicazione:
2023
Citazione:
Contractions of hyper-Kähler fourfolds and the Brauer group / B. van Geemen, G. Kapustka. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 412:(2023), pp. 108814.1-108814.52. [10.1016/j.aim.2022.108814]
Abstract:
We study the geometry of exceptional loci of birational contractions of hyper-Kähler fourfolds that are of K3[2]-type. These loci are conic bundles over K3 surfaces and we determine their classes in the Brauer group. For this we use the results on twisted sheaves on K3 surfaces, on contractions and on the corresponding Heegner divisors. For a general K3 surface of fixed degree there are three (T-equivalence) classes of order two Brauer group elements. The elements in exactly two of these classes are represented by conic bundles on such fourfolds. We also discuss various examples of such conic bundles.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Birational maps; Brauer groups; Hyper-Kähler varieties
Elenco autori:
B. van Geemen, G. Kapustka
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