A sublinear bound for the regularity of subspace arrangements

2026/07/21 by Xin Hong, Yi-Song Huang, Manolis Tsakiris
#math.AC #math.AG

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Abstract

Let X be the union of k generic linear spaces in \PPⁿ of codimension at least 2. We prove that the Castelnuovo-Mumford regularity of the vanishing ideal of X grows in order not more than √(k), and that this is an order-tight bound when the codimension equals 2.

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