Birational Geometry of Singular Moduli Spaces of O'Grady TypeCiaran Meachan, Ziyu Zhang
Following Bayer and Macrì, we study the birational geometry of singular moduli spaces M of sheaves on a K3 surface X which admit symplectic resolutions. More precisely, we use the BayerMacrì map from the space of Bridgeland stability conditions Stab(X) to the cone of movable divisors on M to relate wallcrossing in Stab(X) to birational transformations of M. We give a complete classification of walls in Stab(X) and show that every birational model of M obtained by performing a finite sequence of flops from M appears as a moduli space of Bridgeland semistable objects on X. An essential ingredient of our proof is an isometry between the orthogonal complement of a Mukai vector inside the algebraic Mukai lattice of X and the NéronSeveri lattice of M which generalises results of Yoshioka, as well as Perego and Rapagnetta. Moreover, this allows us to conclude that the symplectic resolution of M is deformation equivalent to the 10dimensional irreducible holomorphic symplectic manifold found by O'Grady. Document Actions 
