  We show that the moduli stacks of semistable sheaves on smooth projective
varieties are analytic locally on their coarse moduli spaces described in terms
of representations of the associated Ext-quivers with convergent relations.
When the underlying variety is a Calabi-Yau 3-fold, our result describes the
above moduli stacks as critical locus analytic locally on the coarse moduli
spaces. The results in this paper will be applied to the wall-crossing formula
of Gopakumar-Vafa invariants defined by Maulik and the author.
