Moduli problems of sheaves associated with oriented trees

Abstract

To every oriented tree, we associate a moduli problem for sheaves over a projective manifold $X$. We define the corresponding notion of semistability and establish the existence of moduli spaces. Applying the results to the tree *->*, we obtain a GIT construction for the moduli space of holomorphic triples of Bradlow and Garcia-Prada.

Revised version contains streamlined notation and updated introduction. The paper will appear in "Algebras and Representation Theory"