Work

On the minimal free resolution of the Rees algebra of some monomial ideals

Year: 2025

Type: article

Abstract: We give a complete description of the defining ideal $$\mathcal {R}(I)$$ R ( I ) of the Rees algebra of any monomial ideal I minimally generated by three monomials in two variables. We give a Gröbner basis and a complete explicit description of the minimal free resolution of $$\mathcal {R}(I)$$ R ( I ) based on arithmetical properties of the generators of the ideal I . We also present algorithms for the computation of $$\mathcal {R}(I)$$ R ( I ) and its minimal free resolution. These results extend and generalize previous work by Cox and by Cortadellas and D’Andrea on parametrizations of monomial plane curves.

Source: Applicable Algebra in Engineering Communication and Computing

DOI: 10.1007/s00200-025-00680-y

Authors: Rodrigo Iglesias, Matthias Orth, Eduardo Sáenz-de-Cabezón, Werner M. Seiler

Institutions: Universidad de La Rioja, University of Kassel

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Universidad de La Rioja, Agencia Estatal de Investigación