Academic Journal
Versal dg deformation of Calabi–Yau manifolds
| Title: | Versal dg deformation of Calabi–Yau manifolds |
|---|---|
| Authors: | Hayato Morimura |
| Source: | Journal of Algebra. 697:243-311 |
| Publication Status: | Preprint |
| Publisher Information: | Elsevier BV, 2026. |
| Publication Year: | 2026 |
| Subject Terms: | 14J32, FOS: Mathematics, 0101 mathematics, Algebraic Geometry, 01 natural sciences, Algebraic Geometry (math.AG) |
| Description: | We prove the equivalence of the deformation theory for a higher dimensional Calabi--Yau manifold and that for its dg category of perfect complexes by giving a natural isomorphism of the deformation functors. As a consequence, 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. Namely, given a pair of derived-equivalent higher dimensional Calabi--Yau manifolds, the dg categories of perfect complexes of their algebraic deformations over a common base, which always exist, become quasi-equivalent close to effectivizations. Then the base change along the corresponding first order approximation yields quasi-equivalent versal Morita deformations. We introduce the generic fiber of the versal Morita deformation as a Drinfeld quotient, which is quasi-equivalent to the dg category of perfect complexes on the generic fiber of the versal deformation. 47 pages; v3: Corrected errors in Section 6. Minor changes here and there |
| Document Type: | Article |
| Language: | English |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2026.02.031 |
| DOI: | 10.48550/arxiv.2111.11778 |
| Access URL: | https://arxiv.org/abs/2111.11778 http://arxiv.org/abs/2111.11778 |
| Rights: | CC BY |
| Accession Number: | edsair.doi.dedup.....9052bc5e8097be6d3d7f8fd15967c033 |
| Database: | OpenAIRE |
| ISSN: | 00218693 |
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| DOI: | 10.1016/j.jalgebra.2026.02.031 |