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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2407.05072 |
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| _version_ | 1866916704364265472 |
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| author | Sheng, Richie Tribone, Tim |
| author_facet | Sheng, Richie Tribone, Tim |
| contents | Consider a pair of elements $f$ and $g$ in a commutative ring $Q$. Given a matrix factorization of $f$ and another of $g$, the tensor product of matrix factorizations, which was first introduced by Knörrer and later generalized by Yoshino, produces a matrix factorization of the sum $f+g$. We will study the tensor product of $d$-fold matrix factorizations, with a particular emphasis on understanding when the construction has a non-trivial direct sum decomposition. As an application of our results, we construct indecomposable maximal Cohen-Macaulay and Ulrich modules over hypersurface domains of a certain form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05072 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor products of $d$-fold matrix factorizations Sheng, Richie Tribone, Tim Commutative Algebra 13C14, 13C13, 13H10, 13F25 Consider a pair of elements $f$ and $g$ in a commutative ring $Q$. Given a matrix factorization of $f$ and another of $g$, the tensor product of matrix factorizations, which was first introduced by Knörrer and later generalized by Yoshino, produces a matrix factorization of the sum $f+g$. We will study the tensor product of $d$-fold matrix factorizations, with a particular emphasis on understanding when the construction has a non-trivial direct sum decomposition. As an application of our results, we construct indecomposable maximal Cohen-Macaulay and Ulrich modules over hypersurface domains of a certain form. |
| title | Tensor products of $d$-fold matrix factorizations |
| topic | Commutative Algebra 13C14, 13C13, 13H10, 13F25 |
| url | https://arxiv.org/abs/2407.05072 |