Poset Resolutions of Monomial Ideals

Details Poset Resolutions of Monomial Ideals Poset Resolutions of Monomial Ideals

2008-06-27

arxiv.org/abs/0806.4532v1

Mathematics

Commutative Algebra

26 pages, with an appendix by Alexandre Tchernev

Scientific paper

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.

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