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arXiv · 2609.00758

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 K\"ahler $n$-fold, $n\ge3,$ 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, $n\ge3,$ 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.'

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Yohsuke Imagi. 2026-09-01. Deformations of Compact Calabi--Yau and Fano Varieties with Isolated Singularities. https://arxiv.org/abs/2609.00758

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