2012/11/22 by Hernan de Alba Casillas, Casillas, Hernan de Alba, Marcel Moralès +2
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Topological and Geometric Data Analysis #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.1211.5364
openalex publication_date 2012/11/22 · arxiv created 2012/12/01 · arxiv updated 2012/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
M. Morales introduced a family of binomial ideals that are binomial extensions of square free monomial ideals. Let I⊂ \si be a square free monomial ideal and J⊂\sis a sum of scroll ideals with some extra conditions, we define the binomial extension of I as \B=I+J⊂ \sis. We set p2(\B) the minimal i∈\N such that there exists j>2 such that βi,i+j(\B)≠ 0. In the case where J=0, Fröberg characterized combinatorally the case p2(I)=∞; later Eisenbud et al. solved the case p2(I)<∞. We obtain a similar result as Fröberg for the binomial extensions and we find lower and upper bounds of p2(\B) for some families of binomial extensions in combinatorial terms as Eisenbud et al. With some additional hypothesis we can compute p2(\B).