Tate Resolutions and Weyman Complexes
David Cox, Evgeny Materov
TL;DR
This paper develops a framework connecting Tate resolutions and Weyman complexes for coherent sheaves on projective spaces, providing explicit constructions and applications to Fourier-Mukai transforms.
Contribution
It introduces generalized Weyman complexes linked to Tate resolutions and details their dependence on differentials, extending to sheaves on projective varieties.
Findings
Explicit construction of Weyman complexes from Tate resolutions
Description of differential dependence in Weyman complexes
Application to Fourier-Mukai transforms for coherent sheaves
Abstract
We construct generalized Weyman complexes for coherent sheaves on projective space and describe explicitly how the differential depend on the differentials in the correpsonding 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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Nonlinear Waves and Solitons