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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.01641 |
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| _version_ | 1866914526493933568 |
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| author | Lehmann, Alessandro Sibilla, Nicolò |
| author_facet | Lehmann, Alessandro Sibilla, Nicolò |
| contents | We prove a generalization of Orlov's theorem for matrix factorizations with $n$ steps. Let $X$ be a regular scheme, $W\colon X\to \mathbb{A}^1$ a flat morphism and $D:=W^{-1}(0)$ its central fiber. We construct an appropriate triangulated category of matrix factorizations with $n$-steps and show that it is equivalent to the singularity category of the root stack $\sqrt[n]{(X, D)}$. We also show that this category admits a semiorthogonal decomposition into $n-1$ copies of the usual (absolute derived) category of matrix factorizations with $2$ steps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01641 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Orlov theorem for matrix factorizations with multiple factors Lehmann, Alessandro Sibilla, Nicolò Algebraic Geometry Algebraic Topology Rings and Algebras 14F08 (Primary), 16E65, 18G80 (Secondary) We prove a generalization of Orlov's theorem for matrix factorizations with $n$ steps. Let $X$ be a regular scheme, $W\colon X\to \mathbb{A}^1$ a flat morphism and $D:=W^{-1}(0)$ its central fiber. We construct an appropriate triangulated category of matrix factorizations with $n$-steps and show that it is equivalent to the singularity category of the root stack $\sqrt[n]{(X, D)}$. We also show that this category admits a semiorthogonal decomposition into $n-1$ copies of the usual (absolute derived) category of matrix factorizations with $2$ steps. |
| title | An Orlov theorem for matrix factorizations with multiple factors |
| topic | Algebraic Geometry Algebraic Topology Rings and Algebras 14F08 (Primary), 16E65, 18G80 (Secondary) |
| url | https://arxiv.org/abs/2605.01641 |