Schemes Supported on the Singular Locus of a Hyperplane Arrangement in Pn

Juan Migliore; Uwe Nagel; Henry Schenck

doi:10.1093/imrn/rnaa113

Schemes Supported on the Singular Locus of a Hyperplane Arrangement in Pn

Juan Migliore
, Uwe Nagel
, Henry Schenck

Mathematics

Producción científica: Article › revisión exhaustiva

1 Cita (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	140-170
Número de páginas	31
Publicación	International Mathematics Research Notices
Volumen	2022
N.º	1
DOI	https://doi.org/10.1093/imrn/rnaa113
Estado	Published - ene 1 2022

Nota bibliográfica

Publisher Copyright:
© The Author(s) 2020.

Financiación

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.].

Financiadores	Número del financiador
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

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10.1093/imrn/rnaa113

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Schemes Supported on the Singular Locus of a Hyperplane Arrangement in Pn

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