Abstract
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.
Original language | English |
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Pages (from-to) | 140-170 |
Number of pages | 31 |
Journal | International Mathematics Research Notices |
Volume | 2022 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 2022 |
Bibliographical note
Funding Information:This work was supported by the Simons Foundation [309556 to J.M., 317096 and 636513 U.N.]; and
Funding Information:
the National Science Foundation [1818646 to H.S.].
Publisher Copyright:
© The Author(s) 2020.
ASJC Scopus subject areas
- Mathematics (all)