The special Brauer group and twisted Picard varieties

Published 6 Oct 2023 in math.AG | (2310.04032v2)

Abstract: We generalise the notion of the Tate-Shafarevich group of an elliptic K3 surface with a section to the Tate-Shafarevich group of a K3 surface endowed with a linear system. The construction, which uses Grothendieck's special Brauer group, provides an efficient way to deal with moduli spaces of twisted sheaves supported on curves in a K3 surface.

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