Simplicial complexes and matroids with vanishing $T^2$
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916657498161152 |
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| author | Constantinescu, Alexandru Klein, Patricia Nguyen, Thai Thanh Singh, Anurag Venturello, Lorenzo |
| author_facet | Constantinescu, Alexandru Klein, Patricia Nguyen, Thai Thanh Singh, Anurag Venturello, Lorenzo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simplicial complexes and matroids with vanishing $T^2$ Constantinescu, Alexandru Klein, Patricia Nguyen, Thai Thanh Singh, Anurag Venturello, Lorenzo Combinatorics Commutative Algebra Algebraic Geometry 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. |
| title | Simplicial complexes and matroids with vanishing $T^2$ |
| topic | Combinatorics Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2406.02440 |