%0 Journal Article
%T A Note on Formality and Singularities of Moduli Spaces
%A Ziyu Zhang
%J Mathematics
%D 2010
%I arXiv
%X This paper studies formality of the differential graded algebra $RHom(E,E)$, where $E$ is a semistable sheaf on a K3 surface. The main tool is Kaledin's theorem on formality in families. For a large class of sheaves $E$, this DG algebra is formal, therefore we have an explicit description of the singularity type of the moduli space of semistable sheaves at the point represented by $E$. This paper also explains why Kaledin's theorem fails to apply in the remaining case.
%U http://arxiv.org/abs/1011.4689v1