| After reviewing the fundamentals on moduli spaces of sheaves on K3 surfaces, local structures and global properties of singular moduli spaces are studied. Generalizing Lehn and Sorger's theorem, we prove that when divisibility of Mukai vector is at most 3, every singular point in the moduli space has an analytic open neighborhood that is a quotient of a quadratic singularity by the stabilizer group of this point. Generalizing Yoshioka's theorem, we prove that when the greatest common divisor of the rank and first Chern class is 2, two moduli spaces of identical dimensions can be connected by deformations and birational maps. |
