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arXiv · 1806.00457

Castelnuovo-Mumford regularity up to symmetry

Dinh Van Le·Uwe Nagel·Hop D. Nguyen·Tim Roemer
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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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Dinh Van Le, Uwe Nagel, Hop D. Nguyen, Tim Roemer. 2018-06-01. Castelnuovo-Mumford regularity up to symmetry. https://doi.org/10.1093/imrn/rnz382

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