Tate resolutions and Weyman complexes

David A. Cox and Evgeny Materov

Vol. 252 (2011), No. 1, 51–68

DOI: 10.2140/pjm.2011.252.51

Abstract

We construct generalized Weyman complexes for coherent sheaves on projective space and describe explicitly how the differentials depend on the differentials in the corresponding Tate resolution. We apply this to define the Weyman complex of a coherent sheaf on a projective variety and explain how certain Weyman complexes can be regarded as Fourier–Mukai transforms.

Keywords

Tate resolution, Weyman complex

Mathematical Subject Classification 2000

Primary: 14F05

Secondary: 13D02

Milestones

Received: 15 June 2010

Accepted: 8 February 2011

Published: 8 October 2011