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

Let I1,,In be ideals generated by linear forms in a polynomial ring over an infinite field and let J = I1In. 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 JP, where P is a certain poset ideal associated to the underlying subspace arrangement.

subspace arrangements, free resolutions
Mathematical Subject Classification
Primary: 13D02
Received: 23 November 2020
Revised: 8 April 2021
Accepted: 24 July 2021
Published: 16 August 2022
Aldo Conca
Dipartimento di Matematica
Università di Genova
Manolis C. Tsakiris
Dipartimento di Matematica
Università di Genova
Academy of Mathematics and Systems Science
Chinese Academy of Sciences