2004/05/29 by D. Kaledin, Kaledin, D., Manfred Lehn +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG
paper · pdf · doi:10.48550/arxiv.math/0405575
28 pages, LaTeX2e. Final version, to appear in MMJ
openalex publication_date 2004/05/29 · arxiv created 2007/03/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the local structure of the singularity in the moduli space of sheaves on a K3 surface which has been resolved by K O'Grady in his construction of new examples of hyperkaehler manifolds. In particular, we identify the singularity with the closure of a certain nilpotent orbit in the coadjoint representation of the group Sp(4). We also prove that the moduli spaces for some other sets of numerical parameters do not admit a smooth symplectic resolution of singularities.