Subcomplexes of Certain Free Resolutions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909439531941888 |
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| author | Banks, Maya Sobieska, Aleksandra |
| author_facet | Banks, Maya Sobieska, Aleksandra |
| contents | What are the subcomplexes of a free resolution? This question is simple to state, but the naive approach leads to a computational quagmire that is infeasible even in small cases. In this paper, we invoke the Bernstein--Gelfand--Gelfand (BGG) correspondence to address this question for free resolutions given by two well-known complexes, the Koszul and the Eagon--Northcott. This novel approach provides a complete characterization of the ranks of free modules in a subcomplex in the Koszul case and imposes numerical restrictions in the Eagon--Northcott case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_15137 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Subcomplexes of Certain Free Resolutions Banks, Maya Sobieska, Aleksandra Commutative Algebra 13D02, 13D40 What are the subcomplexes of a free resolution? This question is simple to state, but the naive approach leads to a computational quagmire that is infeasible even in small cases. In this paper, we invoke the Bernstein--Gelfand--Gelfand (BGG) correspondence to address this question for free resolutions given by two well-known complexes, the Koszul and the Eagon--Northcott. This novel approach provides a complete characterization of the ranks of free modules in a subcomplex in the Koszul case and imposes numerical restrictions in the Eagon--Northcott case. |
| title | Subcomplexes of Certain Free Resolutions |
| topic | Commutative Algebra 13D02, 13D40 |
| url | https://arxiv.org/abs/2112.15137 |