On the existence of a symplectic desingularization of some moduli spaces of sheaves on a K3 surface

Young-Hoon Kiem
2005 Compositio Mathematica  
Let M c be the moduli space of semistable torsion-free sheaves of rank 2 with Chern classes c 1 = 0 and c 2 = c over a K3 surface with generic polarization. When c = 2n 4 is even, M c is a singular projective variety which admits a symplectic form, called the Mukai form, on the smooth part. A natural question raised by O'Grady asks if there exists a desingularization on which the Mukai form extends everywhere nondegenerately. In this paper we show that such a desingularization does not exist
more » ... n does not exist for many even integers c by computing the stringy Euler numbers.
doi:10.1112/s0010437x05001272 fatcat:zzlqvibwavbcrosjgrnz5dknle