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Robert Friedman ; Radu Laza - Deformations of some local Calabi-Yau manifolds
epiga:10899 - Épijournal de Géométrie Algébrique, November 5, 2024, Special volume in honour of Claire Voisin - https://doi.org/10.46298/epiga.2024.10899Deformations of some local Calabi-Yau manifoldsArticle
We study deformations of certain crepant resolutions of isolated rational Gorenstein singularities. After a general discussion of the deformation theory, we specialize to dimension $3$ and consider examples which are good (log) resolutions as well as the case of small resolutions. We obtain some partial results on the classification of canonical threefold singularities that admit good crepant resolutions. Finally, we study a noncrepant example, the blowup of a small resolution whose exceptional set is a smooth curve.
Comment: 35 pages, 3 figures; v6 - final version
Source: arXiv.org:2203.11738
Volume: Special volume in honour of Claire Voisin
Published on: November 5, 2024
Accepted on: May 31, 2024
Submitted on: February 2, 2023
Keywords: Mathematics - Algebraic Geometry, 14J32, 14B07, 32S30, 14E15, 32S45
Funding:
- Source : OpenAIRE Graph
- K-Trivial Varieties - Degenerations, Automorphisms, and Periods; Funder: National Science Foundation; Code: 2101640
Classifications
Mathematics Subject Classification 20201
- 14B07 - Deformations of singularities
- 14E15 - Global theory and resolution of singularities (algebro-geometric aspects)
- 14J32 - Calabi-Yau manifolds (algebro-geometric aspects)
- 32S30 - Deformations of complex singularities; vanishing cycles
- 32S45 - Modifications; resolution of singularities (complex-analytic aspects)
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