A Constructive Method for Standard Borel Fixed Submodules with Given Extremal Betti Numbers

Marilena Crupi
Additional contact information
Marilena Crupi: Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale Ferdinando Stagno d’Alcontres 31, 98166 Messina, Italy

Mathematics, 2017, vol. 5, issue 4, 1-26

Abstract: Let S be a polynomial ring in n variables over a field K of any characteristic. Given a strongly stable submodule M of a finitely generated graded free S -module F , we propose a method for constructing a standard Borel-fixed submodule M ˜ of F so that the extremal Betti numbers of M , values as well as positions, are preserved by passing from M to M ˜ . As a result, we obtain a numerical characterization of all possible extremal Betti numbers of any standard Borel-fixed submodule of a finitely generated graded free S -module F .

Keywords: graded modules; monomial modules; minimal graded resolution; extremal Betti numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/5/4/56/pdf (application/pdf)
https://www.mdpi.com/2227-7390/5/4/56/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:5:y:2017:i:4:p:56-:d:117160

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().