The first cotangent cohomology module for matroids
William Brehm
Freie Universität Berlin, GermanyAlexandru Constantinescu
Freie Universität Berlin, Germany
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Abstract
We find a combinatorial formula which computes the first cotangent cohomology module of Stanley–Reisner rings associated to matroids. For arbitrary simplicial complexes we provide upper bounds for the dimensions of the multigraded components of . For specific degrees we prove that these bounds are reached if and only if the simplicial complex is a matroid, obtaining thus a new characterization for matroids. Furthermore, the graded first cotangent cohomology turns out to be a complete invariant for nondiscrete matroids.
Cite this article
William Brehm, Alexandru Constantinescu, The first cotangent cohomology module for matroids. J. Comb. Algebra 7 (2023), no. 3/4, pp. 327–345
DOI 10.4171/JCA/73