# Moscow Mathematical Journal

Volume 12, Issue 4, October–December 2012 pp. 863–879.

A Note on Formality and Singularities of Moduli Spaces**Authors**: Ziyu Zhang

**Author institution:**Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany

**Summary:**This paper studies formality of the differential graded algebra $\mathrm{RHom}^{\bullet}(E,E)$, 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.

2010 Mathematics Subject Classification. 14D20

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