Equivariant Primary Decomposition and Toric Sheaves

  title={Equivariant Primary Decomposition and Toric Sheaves},
  author={Markus Perling and Guenther Trautmann},
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 toric sheaves over toric varieties. Comparing these decompositions with primary decompositions of graded and fine graded modules over the homogeneous coordinate ring, we show that these are equivalent for smooth toric varieties.