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arXiv · 2112.15137

Subcomplexes of Certain Free Resolutions

Maya Banks·Aleksandra Sobieska
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Abstract

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.

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Maya Banks, Aleksandra Sobieska. 2021-12-30. Subcomplexes of Certain Free Resolutions. https://doi.org/10.1017/nmj.2024.7

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