Linear resolutions of powers and products
| Autor(en): | Bruns, W. Conca, A. |
Stichwörter: | Determinantal ideal; Gröbner basis; Ideal of linear forms; Koszul algebra; Linear resolution; Polymatroidal ideal; Primary decomposition; Rees algebra; Regularity; Toric deformation | Erscheinungsdatum: | 2017 | Herausgeber: | Springer International Publishing | Journal: | Singularities and Computer Algebra: Festschrift for Gert-Martin Greuel on the Occasion of his 70th Birthday | Startseite: | 47 | Seitenende: | 69 | Zusammenfassung: | The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: Every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: Polymatroidal ideals, ideals generated by linear forms, and Borel-fixed ideals of maximal minors. The main tools are Gröbner bases and Sagbi deformation. © Springer International Publishing Switzerland 2017. |
ISBN: | 9783319288291 9783319288284 |
DOI: | 10.1007/978-3-319-28829-1_3 | Externe URL: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85019986580&doi=10.1007%2f978-3-319-28829-1_3&partnerID=40&md5=6da47f00bde60a0f188ca87e08631cef |
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