Poset Resolutions of Monomial Ideals

Timothy B. P. Clark

Poset Resolutions of Monomial Ideals

Commutative Algebra 2008-06-30 v1

Authors: Timothy B. P. Clark

Abstract

We introduce the class of lattice-linear monomial ideals and use the LCM-lattice to give an explicit construction for their minimal free resolution. The class of lattice-linear ideals includes (among others) the class of monomial ideals with linear free resolution and the class of Scarf monomial ideals. Our main tool is a new construction by Tchernev that produces from a map of posets $\eta:P\lra\mbb{N}^n$ a sequence of multigraded modules and maps.

Keywords

monomial ideals and free resolutions ideal theory lattice theory

Cite

@article{arxiv.0806.4532,
  title  = {Poset Resolutions of Monomial Ideals},
  author = {Timothy B. P. Clark},
  journal= {arXiv preprint arXiv:0806.4532},
  year   = {2008}
}

Comments

26 pages, with an appendix by Alexandre Tchernev

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