@article{0801eeec2f85414b87c78e2992c9d92e,
title = "Depth and regularity modulo a principal ideal",
abstract = "We study the relationship between depth and regularity of a homogeneous ideal I and those of (I, f) and I : f, where f is a linear form or a monomial. Our results have several interesting consequences on depth and regularity of edge ideals of hypergraphs and of powers of ideals.",
keywords = "Chordal graph, Depth, Edge ideal, Monomial ideal, Powers of an ideal, Regularity, Very well-covered graph",
author = "Giulio Caviglia and H{\`a}, {Huy T{\`a}i} and J{\"u}rgen Herzog and Manoj Kummini and Naoki Terai and Trung, {Ngo Viet}",
note = "Funding Information: Acknowledgements Giulio Caviglia is partially supported by the Simons Foundation (Grant #209661). Huy T{\`a}i H{\`a} is partially supported by the Simons Foundation (Grant #279786). Ngo Viet Trung is partially supported by Vietnam National Foundation for Science and Technology Development (Grant #101.04-2017.19) and the project VAST.HTQT.NHAT.1/16-18. The main part of this work was done during research stays of the authors at the American Institute of Mathematics in the SQuaRE program “Ordinary powers and symbolic powers” during the period 2012–2014. The authors are grateful to S. A. Seyed Fakhari for pointing out a mistake of Theorem 5.1 in the first version of this paper and to an anonymous referee for mentioning that Lemma 4.1(i) and (ii) were already proved in [31] and [32], respectively. Funding Information: Giulio Caviglia is partially supported by the Simons Foundation (Grant #209661). Huy T?i H? is partially supported by the Simons Foundation (Grant #279786). Ngo Viet Trung is partially supported by Vietnam National Foundation for Science and Technology Development (Grant #101.04-2017.19) and the project VAST.HTQT.NHAT.1/16-18. The main part of this work was done during research stays of the authors at the American Institute of Mathematics in the SQuaRE program ?Ordinary powers and symbolic powers? during the period 2012?2014. The authors are grateful to S. A. Seyed Fakhari for pointing out a mistake of Theorem 5.1 in the first version of this paper and to an anonymous referee for mentioning that Lemma 4.1 (i) and (ii) were already proved in [31] and [32], respectively.",
year = "2019",
month = feb,
day = "15",
doi = "10.1007/s10801-018-0811-9",
language = "English",
volume = "49",
journal = "Journal of Algebraic Combinatorics",
issn = "0925-9899",
publisher = "Springer Netherlands",
number = "1",
}