On k-rational and k-Du Bois local complete intersections

Mustaţă, Mircea; Popa, Mihnea

doi:10.48550/arxiv.2207.08743

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…The k-Du Bois and k-rational singularities, natural extensions of Du Bois and rational singularities, respectively (the case 𝑘 = 0), were recently introduced by [MOPW23], [JKSY22], [KL20], [FL22c] and [MP22]. The relevance of these classes of singularities (especially for 𝑘 = 1) to the deformation theory of singular Calabi-Yau and Fano varieties is discussed in [FL22a], which additionally singles out the kliminal singularities (for 𝑘 = 1) as particularly relevant to the deformation theory of such varieties.…”

Section: K-du Bois K-rational and K-liminal Singularitiesmentioning

confidence: 99%

Deformations of Calabi–Yau varieties withk-liminal singularities

Friedman,

Laza

2024

Forum of Mathematics, Sigma

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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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Section: K-du Bois K-rational and K-liminal Singularitiesmentioning

confidence: 99%

Deformations of Calabi–Yau varieties withk-liminal singularities

Friedman,

Laza

2024

Forum of Mathematics, Sigma

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“…k-Du Bois, k rational, and k-liminal singularities. The k-Du Bois and k-rational singularities, natural extensions of Du Bois and rational singularities respectively (case k = 0), were recently introduced by [MOPW21], [JKSY22], [KL20], [FL22b], and [MP22]. The relevance of these classes of singularities (especially for k = 1) to the deformation theory of singular Calabi-Yau and Fano varieties is discussed in [FL22a], which additionally singles out the k-liminal singularities (for k = 1) as particularly relevant to the deformation theory of such varieties.…”

Section: Introductionmentioning

confidence: 99%

Deformations of Calabi-Yau varieties with $k$-liminal singularities

Friedman¹,

Laza²

2023

Preprint

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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.

show abstract

On k-rational and k-Du Bois local complete intersections

Cited by 2 publications

References 7 publications

Deformations of Calabi–Yau varieties withk-liminal singularities

Deformations of Calabi–Yau varieties withk-liminal singularities

Deformations of Calabi-Yau varieties with $k$-liminal singularities

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