Rocky Mountain Journal of Mathematics

Constructing monomial ideals with a given minimal resolution

Sonja Mapes and Lindsay C. Piechnik

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Abstract

This paper gives a description of various recent results, which construct monomial ideals with a given minimal free resolution. We show that these results are all instances of coordinatizing a finite atomic lattice, as found in~\cite {mapes}. Subsequently, we explain how, in some of these cases \cite {Faridi, Floystad1} where questions still remain, this point of view can be applied. We also prove an equivalence for trees between the notion of \textit {maximal} defined in~\cite {Floystad1} and the notion of being maximal in a Betti stratum.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 6 (2017), 1963-1985.

Dates
First available in Project Euclid: 21 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1511254960

Digital Object Identifier
doi:10.1216/RMJ-2017-47-6-1963

Mathematical Reviews number (MathSciNet)
MR3725252

Zentralblatt MATH identifier
06816578

Subjects
Primary: 13D02: Syzygies, resolutions, complexes

Keywords
Monomial ideal minimal free resolution lcm-lattice cellular resolution Scarf ideal

Citation

Mapes, Sonja; Piechnik, Lindsay C. Constructing monomial ideals with a given minimal resolution. Rocky Mountain J. Math. 47 (2017), no. 6, 1963--1985. doi:10.1216/RMJ-2017-47-6-1963. https://projecteuclid.org/euclid.rmjm/1511254960


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