On the minimal free resolution of the Rees algebra of tri-generated bivariate monomial ideals

2024/01/21 by Iglesias, Rodrigo, Orth, Matthias, Sáenz-de-Cabezón, Eduardo +1
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2401.11558

Abstract

Let I be a monomial ideal in two variables generated by three monomials and let R(I) be its Rees ideal. We describe an algorithm to compute the minimal generating set of R(I). Based on the data obtained by this algorithm, we build a graph that encodes the minimal free resolution of R(I). We explicitly describe the modules and differentials on the minimal free resolution of R(I).

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