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arXiv · 2204.05777

The first Cotangent Cohomology Module for Matroids

William Bitsch·Alexandru Constantinescu
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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 T^1. 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.

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William Bitsch, Alexandru Constantinescu. 2022-04-12. The first Cotangent Cohomology Module for Matroids. https://arxiv.org/abs/2204.05777

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