#### Vol. 16, No. 5, 2022

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Resolution of ideals associated to subspace arrangements

### Aldo Conca and Manolis C. Tsakiris

Vol. 16 (2022), No. 5, 1121–1140
##### Abstract

Let ${I}_{1},\dots ,{I}_{n}$ be ideals generated by linear forms in a polynomial ring over an infinite field and let $J={I}_{1}\cdots {I}_{n}$. We describe a minimal free resolution of $J$ and show that it is supported on a polymatroid obtained from the underlying representable polymatroid by means of the so-called Dilworth truncation. Formulas for the projective dimension and Betti numbers are given in terms of the polymatroid as well as a characterization of the associated primes. Along the way we show that $J$ has linear quotients. In fact, we do this for a large class of ideals ${J}_{P}$, where $P$ is a certain poset ideal associated to the underlying subspace arrangement.

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##### Keywords
subspace arrangements, free resolutions
Primary: 13D02
##### Milestones
Revised: 8 April 2021
Accepted: 24 July 2021
Published: 16 August 2022
##### Authors
 Aldo Conca Dipartimento di Matematica Università di Genova Genova Italy Manolis C. Tsakiris Dipartimento di Matematica Università di Genova Genova Italy Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China