Versal dg deformation of Calabi–Yau manifolds
Abstract
For a higher dimensional Calabi–Yau manifold, we prove that deformations and taking dg categories of perfect complexes intertwine in a suitable sense. As a consequence, the two associated deformation theories are canonically equivalent. Moreover, the dg category of perfect complexes on a versal deformation of the original manifold provides a versal Morita deformation of its dg category of perfect complexes. Besides the classical uniqueness up to étale neiborhood of the base, we prove another sort of uniqueness of versal Morita deformations.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Advanced Topics in Algebra
Publication details
- Journal / source
- Journal of Algebra
- Volume
- 697
- Pages
- 243–311
- Publication date
- 10 March 2026
- Language
- EN