Tate Resolutions and Weyman Complexes

2009/07/20 by Cox, David, Materov, Evgeny
#13D02 #14F05 #16E05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.0907.3326

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.

Related

• Deformations and Fourier-Mukai transforms
• Tate Resolutions on Products of Projective Spaces: Cohomology and Direct Image Complexes
• Tate resolutions on toric varieties
• The Horrocks correspondence for coherent sheaves on projective spaces
• Generation and ampleness of coherent sheaves on abelian varieties, with application to Brill-Noether theory