Abstract: We investigate generalized notions of the nerve complex for the facets of a simplicial complex, including how the homologies of these higher nerve complexes determine the depth of the Stanley-Reisner ring $k[\Delta]$ as well as the $f$-vector and $h$-vector of $\Delta$. We then establish relationships between simplicial complexes satisfying Serre's condition $(S_{\ell})$ and the vanishing of reduced homologies of their higher nerve complexes. We examine the behavior of rank selected subcomplexes of balanced $(S_{\ell})$ complexes, and, generalizing results of Stanley and Hibi, we prove that these subcomplexes retain $(S_{\ell})$.
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