Toric sheaves

Trautmann, Günther

Kaiserslautern, Germany

---

Abstract

A toric sheaf is a torus invariant coherent sheaf on a toric variety. Any such sheaf is related to a fine-graded and finitely generated module over the Cox coordinate ring of the variety. A report on recent results on the structure of toric sheaves is given, stressing global primary decompositions and torus invariant resolutions. The existence of a global primary decomposition of an equivariant sheaf is proved in the more general setting for quasi-homogeneous varieties, and is a refinement of an early theorem of Yum-tong Siu.