Equivariant Primary Decomposition and Toric Sheaves

Details Equivariant Primary Decomposition and Toric Sheaves Equivariant Primary Decomposition and Toric Sheaves

2008-02-02

arxiv.org/abs/0802.0257v2

manuscripta math. 132(1-2), 103-143, 2010

Mathematics

Algebraic Geometry

35 pages, requires packages ams*, enumerate, xy; partially rewritten, includes primary decomposition for general varieties adm

Scientific paper

We study global primary decompositions in the category of sheaves on a scheme which are equivariant under the action of an algebraic group. We show that equivariant primary decompositions exist if the group is connected. As main application we consider the case of varieties which are quotients of a quasi-affine variety by the action of a diagonalizable group and thus admit a homogeneous coordinate ring, such as toric varieties. Comparing these decompositions with primary decompositions of graded modules over the homogeneous coordinate ring, we show that these are equivalent if the action of the diagonalizable group is free. We give some specific examples for the case of toric varieties.

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