Hook-decomposable modules and their resolutions
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908965817810944 |
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| author | Mastroianni, Isabella Guerra, Marco Fugacci, Ulderico De Negri, Emanuela |
| author_facet | Mastroianni, Isabella Guerra, Marco Fugacci, Ulderico De Negri, Emanuela |
| contents | We compare several classes of biparameter persistence modules: $γ$-products of monoparameter modules, hook-decomposable modules, modules admitting a Smith-type structure theorem, and modules of projective dimension at most 1. We determine all logical implications among these classes, providing explicit counterexamples showing that the converses fail when appropriate. In particular, $γ$-products (i.e., hook-decomposable modules) form a very small subclass of biparameter modules, precisely the ones for which a structure theorem still holds, thus making explicit the richer structural complexity of the biparameter setting compared to the monoparameter one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23008 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hook-decomposable modules and their resolutions Mastroianni, Isabella Guerra, Marco Fugacci, Ulderico De Negri, Emanuela Algebraic Topology Commutative Algebra We compare several classes of biparameter persistence modules: $γ$-products of monoparameter modules, hook-decomposable modules, modules admitting a Smith-type structure theorem, and modules of projective dimension at most 1. We determine all logical implications among these classes, providing explicit counterexamples showing that the converses fail when appropriate. In particular, $γ$-products (i.e., hook-decomposable modules) form a very small subclass of biparameter modules, precisely the ones for which a structure theorem still holds, thus making explicit the richer structural complexity of the biparameter setting compared to the monoparameter one. |
| title | Hook-decomposable modules and their resolutions |
| topic | Algebraic Topology Commutative Algebra |
| url | https://arxiv.org/abs/2603.23008 |