2008/01/30 by Daniel Huybrechts, Huybrechts, Daniel, Marc Nieper-Wißkirchen +1 · 1 citation
Mathematics · #14J32 #18E30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0801.4747
openalex publication_date 2008/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present results indicating that the decomposition of a Ricci-flat manifold in its irreducible factors is reflected by the derived category of coherent sheaves. More precisely, we prove that a smooth projective variety that is derived equivalent to an abelian variety resp. an irreducible symplectic variety is of the same type. The paper also contains a proof of a conjecure of Caldararu for manifolds with trivial canonical bundle saying that the modified HKR isomorphism for Hochschild homology is compatible with the module structure.