2010/11/21 by Zhang, Ziyu
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1011.4689
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.