Deformations of Calabi–Yau varieties with k-liminal singularities
In: Forum of Mathematics, Sigma, Jg. 12 (2024)
Online
academicJournal
Zugriff:
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 first given in [Fri86]. Subsequently, Rollenske–Thomas [RT09] 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 [FL22a], the linear necessary and sufficient conditions of [Fri86] 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 [RT09] for Calabi–Yau varieties with weighted homogeneous k-liminal hypersurface singularities, a broad class of singularities that includes ordinary double points in odd dimensions.
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Deformations of Calabi–Yau varieties with k-liminal singularities
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Autor/in / Beteiligte Person: | Friedman, Robert ; Laza, Radu |
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Zeitschrift: | Forum of Mathematics, Sigma, Jg. 12 (2024) |
Veröffentlichung: | Cambridge University Press, 2024 |
Medientyp: | academicJournal |
ISSN: | 2050-5094 (print) |
DOI: | 10.1017/fms.2024.44 |
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