Morse resolutions of monomial ideals and Betti splittings
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916597250129920 |
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| author | Montaner, Josep Àlvarez García, María Lucía Aparicio Mafi, Amir |
| author_facet | Montaner, Josep Àlvarez García, María Lucía Aparicio Mafi, Amir |
| contents | We use discrete Morse theory to study free resolutions of monomial ideals in combination with splitting techniques. We establish the minimality of such pruned resolutions for several classes of ideals, including stable and linear quotient ideals. In particular, we unify classical constructions such as the Eliahou-Kervaire and Herzog-Takayama resolutions within the pruned resolution framework. Additionally, we introduce methods to reduce the minimality study of a pruned resolution for an ideal to that of a smaller subideal and present a variant of our pruned resolution for powers of monomial ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Morse resolutions of monomial ideals and Betti splittings Montaner, Josep Àlvarez García, María Lucía Aparicio Mafi, Amir Commutative Algebra We use discrete Morse theory to study free resolutions of monomial ideals in combination with splitting techniques. We establish the minimality of such pruned resolutions for several classes of ideals, including stable and linear quotient ideals. In particular, we unify classical constructions such as the Eliahou-Kervaire and Herzog-Takayama resolutions within the pruned resolution framework. Additionally, we introduce methods to reduce the minimality study of a pruned resolution for an ideal to that of a smaller subideal and present a variant of our pruned resolution for powers of monomial ideals. |
| title | Morse resolutions of monomial ideals and Betti splittings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2502.02122 |