Castelnuovo–Mumford Regularity up to Symmetry

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 the...

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Bibliographic Details
Published in:International mathematics research notices 2021-07, Vol.2021 (14), p.11010-11049
Main Authors: Le, Dinh Van, Nagel, Uwe, Nguyen, Hop D, Römer, Tim
Format: Article
Language:English
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Summary: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.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnz382