Powers of graphs & applications to resolutions of powers of monomial ideals
Commutative Algebra
2021-08-18 v1
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.
Keywords
Cite
@article{arxiv.2108.07703,
title = {Powers of graphs & applications to resolutions of powers of monomial ideals},
author = {Susan M. Cooper and Sabine El Khoury and Sara Faridi and Sarah Mayes-Tang and Susan Morey and Liana M. Sega and Sandra Spiroff},
journal= {arXiv preprint arXiv:2108.07703},
year = {2021}
}