Projective dimension of weakly chordal graphic arrangements
Abe T, Kühne L, Mücksch P, Mühlherr L (Submitted)
ArXiv: 2307.06021.
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| Eingereicht | Englisch
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Einrichtung
Abstract / Bemerkung
A graphic arrangement is a subarrangement of the braid arrangement whose set of hyperplanes is determined by an undirected graph. A classical result due to Stanley, Edelman and Reiner states that a graphic arrangement is free if and only if the corresponding graph is chordal, i.e., the graph has no chordless cycle with four or more vertices. In this article we extend this result by proving that the module of logarithmic derivations of a graphic arrangement has projective dimension at most one if and only if the corresponding graph is weakly chordal, i.e., the graph and its complement have no chordless cycle with five or more vertices.
Erscheinungsjahr
2023
Zeitschriftentitel
ArXiv: 2307.06021
Page URI
https://pub.uni-bielefeld.de/record/2982635
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Abe T, Kühne L, Mücksch P, Mühlherr L. Projective dimension of weakly chordal graphic arrangements. ArXiv: 2307.06021. Submitted.
Abe, T., Kühne, L., Mücksch, P., & Mühlherr, L. (Submitted). Projective dimension of weakly chordal graphic arrangements. ArXiv: 2307.06021. https://doi.org/10.48550/ARXIV.2307.06021
Abe, Takuro, Kühne, Lukas, Mücksch, Paul, and Mühlherr, Leonie. Submitted. “Projective dimension of weakly chordal graphic arrangements”. ArXiv: 2307.06021.
Abe, T., Kühne, L., Mücksch, P., and Mühlherr, L. (Submitted). Projective dimension of weakly chordal graphic arrangements. ArXiv: 2307.06021.
Abe, T., et al., Submitted. Projective dimension of weakly chordal graphic arrangements. ArXiv: 2307.06021.
T. Abe, et al., “Projective dimension of weakly chordal graphic arrangements”, ArXiv: 2307.06021, Submitted.
Abe, T., Kühne, L., Mücksch, P., Mühlherr, L.: Projective dimension of weakly chordal graphic arrangements. ArXiv: 2307.06021. (Submitted).
Abe, Takuro, Kühne, Lukas, Mücksch, Paul, and Mühlherr, Leonie. “Projective dimension of weakly chordal graphic arrangements”. ArXiv: 2307.06021 (Submitted).
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