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Mathematics 2017, 5(4), 56; https://doi.org/10.3390/math5040056

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

Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale Ferdinando Stagno d’Alcontres 31, 98166 Messina, Italy
Academic Editor: Yang-Hui He
Received: 29 May 2017 / Revised: 9 October 2017 / Accepted: 17 October 2017 / Published: 1 November 2017
View Full-Text   |   Download PDF [340 KB, uploaded 1 November 2017]

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. View Full-Text
Keywords: graded modules; monomial modules; minimal graded resolution; extremal Betti numbers graded modules; monomial modules; minimal graded resolution; extremal Betti numbers
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Crupi, M. A Constructive Method for Standard Borel Fixed Submodules with Given Extremal Betti Numbers. Mathematics 2017, 5, 56.

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