Deformations of Calabi-Yau Varieties With Isolated Log Canonical Singularities

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