English

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}
}