Poset Resolutions of Monomial Ideals
Timothy B.P. Clark
TL;DR
This paper introduces lattice-linear monomial ideals and provides an explicit construction for their minimal free resolutions using the LCM-lattice, encompassing ideals with linear resolutions and Scarf ideals.
Contribution
It defines lattice-linear monomial ideals and develops a new construction to explicitly determine their minimal free resolutions.
Findings
Includes classes like monomial ideals with linear resolutions and Scarf ideals.
Provides an explicit, constructive method for minimal free resolutions.
Utilizes a new poset-based construction by Tchernev.
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 a sequence of multigraded modules and maps.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic structures and combinatorial models