TY - JOUR
T1 - Schemes Supported on the Singular Locus of a Hyperplane Arrangement in Pn
AU - Migliore, Juan
AU - Nagel, Uwe
AU - Schenck, Henry
N1 - Publisher Copyright:
© The Author(s) 2020.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - A hyperplane arrangement in Pn is free if R/J is Cohen-Macaulay (CM), where R = k[x0, . . . , xn] and J is the Jacobian ideal. We study the CM-ness of two related unmixed ideals: Jun, the intersection of height two primary components, and √ J, the radical. Under a mild hypothesis, we show these ideals are CM. Suppose the hypothesis fails. For equidimensional curves in P3, the Hartshorne-Rao module measures the failure of CMness and determines the even liaison class of the curve. We show that for any positive integer r, there is an arrangement for which R/Jun (resp. R/ √ J) fails to be CM in only one degree, and this failure is by r. We draw consequences for the even liaison class of Jun or √ J.
AB - A hyperplane arrangement in Pn is free if R/J is Cohen-Macaulay (CM), where R = k[x0, . . . , xn] and J is the Jacobian ideal. We study the CM-ness of two related unmixed ideals: Jun, the intersection of height two primary components, and √ J, the radical. Under a mild hypothesis, we show these ideals are CM. Suppose the hypothesis fails. For equidimensional curves in P3, the Hartshorne-Rao module measures the failure of CMness and determines the even liaison class of the curve. We show that for any positive integer r, there is an arrangement for which R/Jun (resp. R/ √ J) fails to be CM in only one degree, and this failure is by r. We draw consequences for the even liaison class of Jun or √ J.
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U2 - 10.1093/imrn/rnaa113
DO - 10.1093/imrn/rnaa113
M3 - Article
AN - SCOPUS:85127285732
SN - 1073-7928
VL - 2022
SP - 140
EP - 170
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 1
ER -