PreprintarXiv licencearXiv
Lyubeznik numbers of the face rings of simplicial posets
Abstract
For a simplicial poset P, Stanley assigned the face ring AP, which is the quotient of the polynomial ring S:=K[tx | x ∈ P ∖ {0̂ }] by the ideal IP. This is a generalization of Stanley-Reisner rings, but the grading of S is more involved. Building on our previous paper, we further develop and complete the study of the local cohomology modules HIPi(S). In our categorical framework, ExtS(AP, S) ``encodes" all the information of HIPi(S). We treat HIPi(S) in a reasonably explicit way. In particular, Lyubeznik numbers λi,j(AP) can be simply expressed in terms of [ExtS*(ExtS*(AP,S), S)]bf0, and depend only on the homeomorphism class of the underlying space of the CW complex associated with P and char(K).
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BibTeX
@misc{shibata2026lyubeznik,
title = {{Lyubeznik numbers of the face rings of simplicial posets}},
author = {Kosuke Shibata and Kohji Yanagawa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38478},
eprint = {2610.38478},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38478},
}
RIS
TY - UNPB
TI - Lyubeznik numbers of the face rings of simplicial posets
AU - Kosuke Shibata
AU - Kohji Yanagawa
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38478
UR - https://arxiv.org/abs/2610.38478
AB - For a simplicial poset P, Stanley assigned the face ring A_P, which is the quotient of the polynomial ring S:=K[t_x | x ∈ P ∖ {0̂ }] by the ideal I_P. This is a generalization of Stanley-Reisner rings, but the grading of S is more involved. Building on our previous paper, we further develop and complete the study of the local cohomology modules H_I_P^i(S). In our categorical framework, Ext_S(A_P, S) ``encodes" all the information of H_I_P^i(S). We treat H_I_P^i(S) in a reasonably explicit way. In particular, Lyubeznik numbers λ_i,j(A_P) can be simply expressed in terms of [Ext_S^*(Ext_S^*(A_P,S), S)]_bf0, and depend only on the homeomorphism class of the underlying space of the CW complex associated with P and char(K).
ER -