Higher Nerves of Simplicial Complexes
Combinatorics
2019-01-30 v4 Commutative Algebra
Abstract
We investigate generalized notions of the nerve complex for the facets of a simplicial complex. We show that the homologies of these higher nerve complexes determine the depth of the Stanley-Reisner ring as well as the -vector and -vector of . We present, as an application, a formula for computing regularity of monomial ideals.
Cite
@article{arxiv.1710.06129,
title = {Higher Nerves of Simplicial Complexes},
author = {Hailong Dao and Joseph Doolittle and Ken Duna and Bennet Goeckner and Brent Holmes and Justin Lyle},
journal= {arXiv preprint arXiv:1710.06129},
year = {2019}
}
Comments
We rewrite Section 4 to fix some errors and clarify the proofs