Betti numbers of symmetric shifted ideals
| Autor(en): | Biermann, Jennifer de Alba, Hernan Galetto, Federico Murai, Satoshi Nagel, Uwe O'Keefe, Augustine Roemer, Tim Seceleanu, Alexandra |
Stichwörter: | Betti numbers; Equivariant resolution; Linear quotients; Mathematics; MINIMAL FREE RESOLUTION; Shifted ideal; Star configuration; STAR-CONFIGURATION; Symbolic power | Erscheinungsdatum: | 2020 | Herausgeber: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Journal: | JOURNAL OF ALGEBRA | Volumen: | 560 | Startseite: | 312 | Seitenende: | 342 | Zusammenfassung: | We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the class of monomial ideals fixed by this action, they can be considered as an analogue of stable monomial ideals within the class of monomial ideals. We show that a symmetric shifted ideal has linear quotients and compute its (equivariant) graded Betti numbers. As an application of this result, we obtain several consequences for graded Betti numbers of symbolic powers of defining ideals of star configurations. (C) 2020 Elsevier Inc. All rights Inc. All rights reserved. |
ISSN: | 00218693 | DOI: | 10.1016/j.jalgebra.2020.04.037 |
Show full item record
