Moduli of Equivariant and Invariant Sheaves on Toric Varieties

Extending work of Klyachko and Perling, we develop a combinatorial description of pure equivariant sheaves on an arbitrary nonsingular toric

variety X. This combinatorial description can be used to construct moduli spaces of stable equivariant sheaves on X using Geometric Invariant Theory (analogous to techniques used in case of equivariant vector bundles on X by Payne and Perling). We study how the moduli spaces of stable equivariant sheaves on X can be used to explicitly compute the fixed point locus of the moduli space of all stable sheaves on X, i.e. the subscheme of invariant stable sheaves on X.