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arXiv · 2406.02440

Simplicial complexes and matroids with vanishing $T^2$

Alexandru Constantinescu·Patricia Klein·Thai Thanh Nguyen·Anurag Singh·Lorenzo Venturello
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Abstract

We investigate quotients by radical monomial ideals for which $T^2$, the second cotangent cohomology module, vanishes. The dimension of the graded components of $T^2$, and thus their vanishing, depends only on the combinatorics of the corresponding simplicial complex. We give both a complete characterization and a full list of one dimensional complexes with $T^2=0$. We characterize the graded components of $T^2$ when the simplicial complex is a uniform matroid. Finally, we show that $T^2$ vanishes for all matroids of corank at most two and conjecture that all connected matroids with vanishing $T^2$ are of corank at most two.

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Alexandru Constantinescu, Patricia Klein, Thai Thanh Nguyen, Anurag Singh, Lorenzo Venturello. 2024-06-04. Simplicial complexes and matroids with vanishing $T^2$. https://arxiv.org/abs/2406.02440

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