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 |
|---|---|
| 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
Publisher Copyright:© The Author(s) 2020.
Funding
This work was supported by the Simons Foundation [309556 to J.M., 317096 and 636513 U.N.]; and the National Science Foundation [1818646 to H.S.].
| Funders | Funder number |
|---|---|
| Simons Foundation | 636513, 317096, 309556 |
| U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China | 1818646 |
ASJC Scopus subject areas
- General Mathematics