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- W4321277333 abstract "The goal of this paper is to describe certain nonlinear topological obstructions for the existence of first order smoothings of mildly singular Calabi-Yau varieties of dimension at least $4$. For nodal Calabi-Yau threefolds, a necessary and sufficient linear topological condition for the existence of a first order smoothing was given by the first author in 1986. Subsequently, Rollenske-Thomas generalized this picture to nodal Calabi-Yau varieties of odd dimension, by finding a necessary nonlinear topological condition for the existence of a first order smoothing. In a complementary direction, in our recent work, the linear necessary and sufficient conditions for nodal Calabi-Yau threefolds were extended to Calabi-Yau varieties in every dimension with $1$-liminal singularities (which are exactly the ordinary double points in dimension $3$ but not in higher dimensions). In this paper, we give a common formulation of all of these previous results by establishing analogues of the nonlinear topological conditions of Rollenske-Thomas for Calabi-Yau varieties with weighted homogeneous $k$-liminal hypersurface singularities, a broad class of singularities that includes ordinary double points in odd dimensions." @default.
- W4321277333 created "2023-02-18" @default.
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- W4321277333 date "2023-02-16" @default.
- W4321277333 modified "2023-10-05" @default.
- W4321277333 title "Deformations of Calabi-Yau varieties with $k$-liminal singularities" @default.
- W4321277333 doi "https://doi.org/10.48550/arxiv.2302.08488" @default.
- W4321277333 hasPublicationYear "2023" @default.
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