Simplicial Complexes and Matroids with Vanishing $T^2$
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.
Authors
- Alexandru Constantinescu (ORCID: https://orcid.org/0009-0007-1162-5777)
- Lorenzo Venturello (ORCID: https://orcid.org/0000-0002-6797-5270)
- Thái Thành Nguyên (ORCID: https://orcid.org/0000-0002-1697-6193)
- Anurag Singh (ORCID: https://orcid.org/0009-0005-3829-8396)
- Patricia Klein (ORCID: https://orcid.org/0000-0003-4026-6981)
Institutions
- University of Siena (IT)
- Indian Institute of Technology Bhilai (IN)
- Freie Universität Berlin (DE)
- McMaster University (CA)
Publication Details
- Journal
- The Electronic Journal of Combinatorics
- Published
- 2025-04-24
- DOI
- https://doi.org/10.37236/13236
- Primary Topic
- Commutative Algebra and Its Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- National Foundation for Science and Technology Development
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- National Board for Higher Mathematics
- Vietnam Institute for Advanced Study in Mathematics
- Banff International Research Station for Mathematical Innovation and Discovery
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni