Powers of Alexander Duals of Stanley-Reisner Ideals of Chessboard Complexes
Abstract
Let Δm,n be the chessboard complex, and let Jm,n be the Stanley-Reisner ideal of its Alexander dual. We study the symbolic and ordinary powers of Jm,n, focusing on their homological and algebraic invariants. First, we characterize when Jm,n(q) has linear quotients. For the ordinary powers, we give sufficient conditions on m and n for Jm,nq to have linear quotients. We determine the maximal degree of a minimal generator and the Castelnuovo-Mumford regularity of Jm,n(q), obtaining explicit formulas for all q≥2 and showing that both invariants have the same asymptotic slope. We also compute the initial degrees and Waldschmidt constant, proving that α(Jm,n(q)) is a degree-one quasi-polynomial of period two and α̂(Jm,n)=mn/2. Explicit formulas for the v-numbers of symbolic and ordinary powers are obtained. Finally, for every m≥3, we show that Jm,2m−1 is not weakly polymatroidal, disproving a conjecture of Lu and Wang in this setting.
Related
- Homology of non-matching complexes under edge additions and applications to their Stanley-Reisner ideals
- The v-number of powers of ideals associated with chessboard complexes
- Stanley-Reisner Theory in Mixed Characteristic
- Cube-freeness and a square formula for canonical trace ideals of Stanley--Reisner rings
- Characterization of Stanley-Reisner varieties by their automorphism group
BibTeX
@misc{ghosh2026powers,
title = {{Powers of Alexander Duals of Stanley-Reisner Ideals of Chessboard Complexes}},
author = {Arka Ghosh and S. Selvaraja},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37219},
eprint = {2609.37219},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37219},
}
RIS
TY - UNPB
TI - Powers of Alexander Duals of Stanley-Reisner Ideals of Chessboard Complexes
AU - Arka Ghosh
AU - S. Selvaraja
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37219
UR - https://arxiv.org/abs/2609.37219
AB - Let Δ_m,n be the chessboard complex, and let J_m,n be the Stanley-Reisner ideal of its Alexander dual. We study the symbolic and ordinary powers of J_m,n, focusing on their homological and algebraic invariants. First, we characterize when J_m,n^(q) has linear quotients. For the ordinary powers, we give sufficient conditions on m and n for J_m,n^q to have linear quotients. We determine the maximal degree of a minimal generator and the Castelnuovo-Mumford regularity of J_m,n^(q), obtaining explicit formulas for all q≥2 and showing that both invariants have the same asymptotic slope. We also compute the initial degrees and Waldschmidt constant, proving that α(J_m,n^(q)) is a degree-one quasi-polynomial of period two and α̂(J_m,n)=mn/2. Explicit formulas for the v-numbers of symbolic and ordinary powers are obtained. Finally, for every m≥3, we show that J_m,2m−1 is not weakly polymatroidal, disproving a conjecture of Lu and Wang in this setting.
ER -