English

Pruned cellular free resolutions of monomial ideals

Commutative Algebra 2019-10-01 v2 Combinatorics

Abstract

Using discrete Morse theory, we give an algorithm that prunes the excess of information in the Taylor resolution and constructs a new cellular free resolution for an arbitrary monomial ideal. The pruned resolution is not simplicial in general, but we can slightly modify our algorithm in order to obtain a simplicial resolution. We also show that the Lyubeznik resolution fits into our pruning strategy. We finally use our methods to give a different approach to the theory of splitting of monomial ideals.

Keywords

Cite

@article{arxiv.1701.01134,
  title  = {Pruned cellular free resolutions of monomial ideals},
  author = {Josep Àlvarez Montaner and Oscar Fernández-Ramos and Philippe Gimenez},
  journal= {arXiv preprint arXiv:1701.01134},
  year   = {2019}
}

Comments

16 pages. Final version, to appear in Journal of Algebra

R2 v1 2026-06-22T17:41:21.466Z