Linear Maps in Minimal Free Resolutions of Stanley-Reisner Rings

Lukas Katthän
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Lukas Katthän: Goethe-Universität, FB 12–Institut für Mathematik, Postfach 11 19 32, D-60054 Frankfurt am Main, Germany

Mathematics, 2019, vol. 7, issue 7, 1-6

Abstract: In this short note we give an elementary description of the linear part of the minimal free resolution of a Stanley-Reisner ring of a simplicial complex Δ . Indeed, the differentials in the linear part are simply a compilation of restriction maps in the simplicial cohomology of induced subcomplexes of Δ . Along the way, we also show that if a monomial ideal has at least one generator of degree 2, then the linear strand of its minimal free resolution can be written using only ± 1 coefficients.

Keywords: monomial ideal; Stanley-Reisner ring; linear part (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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