| Autor: |
Robert Friedman, Radu Laza |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
Forum of Mathematics, Sigma, Vol 12 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2050-5094 |
| DOI: |
10.1017/fms.2024.44 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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