An EisenbudGoto type inequality for StanleyReisner ideals and simplicial complexes
Abstract
The Leray number of an abstract simplicial complex is the minimal integer $d$ where its induced subcomplexes have trivial homology groups in dimension $d$ or greater. We give an upper bound on the Leray number of a complex in terms of how the facets are attached to each other. We also describe the structure of complexes for the equality of the bound that we found. Through the StanleyReisner correspondence, our results give an EisenbudGoto type inequality for any squarefree monomial ideals. This generalizes Terai's result.
 Publication:

arXiv eprints
 Pub Date:
 August 2023
 DOI:
 10.48550/arXiv.2308.03338
 arXiv:
 arXiv:2308.03338
 Bibcode:
 2023arXiv230803338J
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Topology;
 Mathematics  Combinatorics;
 13F55;
 55U10;
 13D02
 EPrint:
 18 pages, 1 figure