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arXiv · 2306.03755

Deformations of Calabi-Yau varieties with isolated log canonical singularities

Robert Friedman·Radu Laza
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Abstract

Recent progress in the deformation theory of Calabi-Yau varieties $Y$ with canonical singularities has highlighted the key role played by the higher Du Bois and higher rational singularities, and especially by the so-called $k$-liminal singularities for $k\ge 1$. The goal of this paper is to show that certain aspects of this study extend naturally to the $0$-liminal case as well, i.e. to Calabi-Yau varieties $Y$ with Gorenstein log canonical, but not canonical, singularities. In particular, we show the existence of first order smoothings of $Y$ in the case of isolated $0$-liminal hypersurface singularities, and extend Namikawa's unobstructedness theorem for deformations of singular Calabi-Yau threefolds $Y$ with canonical singularities to the case where $Y$ has an isolated $0$-liminal lci singularity under suitable hypotheses. Finally, we describe an interesting series of examples.

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Robert Friedman, Radu Laza. 2023-06-06. Deformations of Calabi-Yau varieties with isolated log canonical singularities. https://doi.org/10.1093/imrn%2Frnaf112

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