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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
Mathematics 2017, 5(4), 56; https://doi.org/10.3390/math5040056
Received: 29 May 2017 / Revised: 9 October 2017 / Accepted: 17 October 2017 / Published: 1 November 2017
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
MDPI and ACS Style

Crupi, M. A Constructive Method for Standard Borel Fixed Submodules with Given Extremal Betti Numbers. Mathematics 2017, 5, 56.

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