Graded Rings and Equivariant Sheaves on Toric Varieties

Details Graded Rings and Equivariant Sheaves on Toric Varieties Graded Rings and Equivariant Sheaves on Toric Varieties

2002-05-29

arxiv.org/abs/math/0205311v1

Math. Nachr. 263-264, 181-197 (2004)

Mathematics

Algebraic Geometry

22 pages, to appear in Mathematische Nachrichten, uses packages ams*, xypic, enumerate

Scientific paper

In this note we derive a formalism for describing equivariant sheaves over toric varieties. This formalism is a generalization of a correspondence due to Klyachko, which states that equivariant vector bundles on toric varieties are equivalent to certain sets of filtrations of vector spaces. We systematically construct the theory from the point of view of graded ring theory and this way we clarify earlier constructions of Kaneyama and Klyachko. We also connect the formalism to the theory of fine-graded modules over Cox' homogeneous coordinate ring of a toric variety. As an application we construct minimal resolutions of equivariant vector bundles of rank two on toric surfaces.

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