Deformations of Calabi-Yau varieties with isolated log canonical singularities

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.

37 pages; final version, to appear in IMRN

References in corpus (7)

• The higher Du Bois and higher rational properties for isolated singularities
• Higher Du Bois and higher rational singularities
• Deformations of Calabi-Yau varieties with $k$-liminal singularities
• Deformations of some local Calabi-Yau manifolds
• On $k$-Du Bois and $k$-rational singularities
• Deformations of I-surfaces with elliptic singularities
• On log minimality of weak K-moduli compactifications of Calabi-Yau varieties