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arXiv · 2108.07703

Powers of graphs & applications to resolutions of powers of monomial ideals

Susan M. Cooper·Sabine El Khoury·Sara Faridi·Sarah Mayes-Tang·Susan Morey·Liana M. Sega·Sandra Spiroff
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Abstract

This paper is concerned with the question of whether geometric structures such as cell complexes can be used to simultaneously describe the minimal free resolutions of all powers of a monomial ideal. We provide a full answer in the case of square-free monomial ideals of projective dimension one, by introducing a combinatorial construction of a family of (cubical) cell complexes whose 1-skeletons are powers of a graph that supports the resolution of the ideal.

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Susan M. Cooper, Sabine El Khoury, Sara Faridi, Sarah Mayes-Tang, Susan Morey, Liana M. Sega, Sandra Spiroff. 2021-08-17. Powers of graphs & applications to resolutions of powers of monomial ideals. https://arxiv.org/abs/2108.07703

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