Fall 2022 Resolutions of ideals of subspace arrangements
Francesca Gandini
J. Commut. Algebra 14(3): 319-338 (Fall 2022). DOI: 10.1216/jca.2022.14.319


Given a collection of t subspaces in an n-dimensional vector space W we can associate to them t linear ideals in the symmetric algebra 𝒮(W). Conca and Herzog showed that the Castelnuovo–Mumford regularity of the product of t linear ideals is equal to t. Derksen and Sidman showed that the Castelnuovo–Mumford regularity of the intersection of t linear ideals is at most t. We show that analogous results hold when we work over the exterior algebra (W) (over a field of characteristic 0). To prove these results we rely on the functoriality of equivariant free resolutions and construct a functor Ω from the category of polynomial functors to itself. The functor Ω transforms resolutions of polynomial functors associated to subspace arrangements over the symmetric algebra to resolutions over the exterior algebra.


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Francesca Gandini. "Resolutions of ideals of subspace arrangements." J. Commut. Algebra 14 (3) 319 - 338, Fall 2022. https://doi.org/10.1216/jca.2022.14.319


Received: 22 July 2019; Revised: 1 August 2020; Accepted: 4 September 2020; Published: Fall 2022
First available in Project Euclid: 7 October 2022

MathSciNet: MR4492994
zbMATH: 1514.13011
Digital Object Identifier: 10.1216/jca.2022.14.319

Primary: 13D02 , 13P20 , 16E05
Secondary: 20C32

Keywords: Castelnuovo–Mumford regularity , equivariant resolution , exterior algebra , subspace arrangement

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium


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Vol.14 • No. 3 • Fall 2022
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