Toric sheaves on smooth projective toric varieties are encoded by polyhedral 'Weil decorations', which are used to construct universal extensions of nef line bundles and a spectral sequence computing sheaf cohomology from reduced cohomology of polyhedral subsets.
Extensions of toric line bundles
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Toric sheaves and polyhedra
Toric sheaves on smooth projective toric varieties are encoded by polyhedral 'Weil decorations', which are used to construct universal extensions of nef line bundles and a spectral sequence computing sheaf cohomology from reduced cohomology of polyhedral subsets.