Castelnuovo-Mumford Regularity up to Symmetry

Dinh Van Le; Uwe Nagel; Hop D. Nguyen; Tim Römer

doi:10.1093/imrn/rnz382

Castelnuovo-Mumford Regularity up to Symmetry

Dinh Van Le, Uwe Nagel, Hop D. Nguyen, Tim Römer

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We study the asymptotic behavior of the Castelnuovo-Mumford regularity along chains of graded ideals in increasingly larger polynomial rings that are invariant under the action of symmetric groups. A linear upper bound for the regularity of such ideals is established. We conjecture that their regularity grows eventually precisely linearly. We establish this conjecture in several cases, most notably when the ideals are Artinian or squarefree monomial.

Original language	English
Pages (from-to)	11010-11049
Number of pages	40
Journal	International Mathematics Research Notices
Volume	2021
Issue number	14
DOIs	https://doi.org/10.1093/imrn/rnz382
State	Published - Jul 1 2021

Bibliographical note

Funding Information:
The 2nd author was partially supported by Simons Foundation grant #317096. The 3rd author was partially supported by Vietnam Academy of Science and Technology (VAST; Project CT 0000.03/19-21), and he acknowledges the support of the International Centre for Research and Postgraduate Training in Mathematics, Institute of Mathematics, VAST (Project ICRTM01_2019.01).

Publisher Copyright:
© 2020 The Author(s) 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

ASJC Scopus subject areas

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abstract = "We study the asymptotic behavior of the Castelnuovo-Mumford regularity along chains of graded ideals in increasingly larger polynomial rings that are invariant under the action of symmetric groups. A linear upper bound for the regularity of such ideals is established. We conjecture that their regularity grows eventually precisely linearly. We establish this conjecture in several cases, most notably when the ideals are Artinian or squarefree monomial.",

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AU - Le, Dinh Van

AU - Nagel, Uwe

AU - Nguyen, Hop D.

AU - Römer, Tim

N1 - Funding Information: The 2nd author was partially supported by Simons Foundation grant #317096. The 3rd author was partially supported by Vietnam Academy of Science and Technology (VAST; Project CT 0000.03/19-21), and he acknowledges the support of the International Centre for Research and Postgraduate Training in Mathematics, Institute of Mathematics, VAST (Project ICRTM01_2019.01). Publisher Copyright: © 2020 The Author(s) 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

PY - 2021/7/1

Y1 - 2021/7/1

N2 - We study the asymptotic behavior of the Castelnuovo-Mumford regularity along chains of graded ideals in increasingly larger polynomial rings that are invariant under the action of symmetric groups. A linear upper bound for the regularity of such ideals is established. We conjecture that their regularity grows eventually precisely linearly. We establish this conjecture in several cases, most notably when the ideals are Artinian or squarefree monomial.

AB - We study the asymptotic behavior of the Castelnuovo-Mumford regularity along chains of graded ideals in increasingly larger polynomial rings that are invariant under the action of symmetric groups. A linear upper bound for the regularity of such ideals is established. We conjecture that their regularity grows eventually precisely linearly. We establish this conjecture in several cases, most notably when the ideals are Artinian or squarefree monomial.

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Castelnuovo-Mumford Regularity up to Symmetry

Abstract

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