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Proceedings of the American Mathematical Society

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Simplicial complexes of small codimension


Authors: Matteo Varbaro and Rahim Zaare-Nahandi
Journal: Proc. Amer. Math. Soc. 147 (2019), 3347-3355
MSC (2010): Primary 13H10, 13F55
DOI: https://doi.org/10.1090/proc/14510
Published electronically: April 8, 2019
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Abstract: We show that $ {\rm CM}_t$ simplicial complexes, a notion generalizing Buchsbaum-ness, of small codimension must have large depth, proving more precise results in the codimension 2 case. In the paper, we show that the $ {\rm CM}_t$ property is a topological invariant of a simplicial complex.


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Matteo Varbaro
Affiliation: Dipartimento di Matematica, Universita’ di Genova, Via Dodecaneso 35, Genova 16146, Italy
Email: varbaro@dima.unige.it

Rahim Zaare-Nahandi
Affiliation: School of Mathematics, Statistics & Computer Science, University of Tehran, Tehran, Iran
Email: rahimzn@ut.ac.ir

DOI: https://doi.org/10.1090/proc/14510
Keywords: Cohen-Macaulay simplicial complex, Buchsbaum simplicial complex, ${CM}_t$ simplicial complex, Serre condition $S_r$, Alexander dual, Eagon-Reiner theorem, Betti diagram, subadditivity, flag simplicial complex
Received by editor(s): July 23, 2018
Received by editor(s) in revised form: December 7, 2018
Published electronically: April 8, 2019
Additional Notes: The second author was supported in part by a grant from the University of Tehran
Communicated by: Claudia Polini
Article copyright: © Copyright 2019 American Mathematical Society