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PreprintCC BY 4.0arXiv

Deformations of Compact Calabi--Yau and Fano Varieties with Isolated Singularities

  • Yohsuke Imagi
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Abstract

Let X be a compact log-canonical Kähler n-fold, n≥3, with trivial canonical sheaf and with isolated singularities. We prove that the generic fibres of a semi-universal deformation of X have Du Bois invariant b1,n−2=0 at the singular points. Under a certain topological hypothesis on X the generic fibres have also link invariant l1,n−2=0. If X is a projective log-canonical n-fold, n≥3, with ample anti-canonical sheaf and with isolated singularities then the generic fibres have b1,n−2=l1,n−2=0 (without the topological hypothesis). These are generalizations of recent results of Tenie `Global smoothing of singular Fano and Calabi--Yau varieties' and an older result of Namikawa `Deformation theory of Calabi--Yau threefolds and certain invariants of singularities.'

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Cite

BibTeXRIS
BibTeX
@misc{imagi2026deformations,
  title = {{Deformations of Compact Calabi--Yau and Fano Varieties with Isolated Singularities}},
  author = {Yohsuke Imagi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00758},
  eprint = {2609.00758},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00758},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Deformations of Compact Calabi--Yau and Fano Varieties with Isolated Singularities
AU  - Yohsuke Imagi
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00758
UR  - https://arxiv.org/abs/2609.00758
AB  - Let X be a compact log-canonical Kähler n-fold, n≥3, with trivial canonical sheaf and with isolated singularities. We prove that the generic fibres of a semi-universal deformation of X have Du Bois invariant b^1,n−2=0 at the singular points. Under a certain topological hypothesis on X the generic fibres have also link invariant l^1,n−2=0. If X is a projective log-canonical n-fold, n≥3, with ample anti-canonical sheaf and with isolated singularities then the generic fibres have b^1,n−2=l^1,n−2=0 (without the topological hypothesis). These are generalizations of recent results of Tenie `Global smoothing of singular Fano and Calabi--Yau varieties' and an older result of Namikawa `Deformation theory of Calabi--Yau threefolds and certain invariants of singularities.'
ER  -