Vol. 16, No. 5, 2022

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 6, 1327–1546
Issue 5, 1025–1326
Issue 4, 777–1024
Issue 3, 521–775
Issue 2, 231–519
Issue 1, 1–230

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Resolution of ideals associated to subspace arrangements

Aldo Conca and Manolis C. Tsakiris

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

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.

Keywords
subspace arrangements, free resolutions
Mathematical Subject Classification
Primary: 13D02
Milestones
Received: 23 November 2020
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