Betti numbers of binomial ideals. (May 2017)

• Record Type: Journal Article
• Authors: de Alba, Hernán; Morales, Marcel
• Is Part Of: Journal of symbolic computation. Volume 80:Part 2(2017)
• Page Start: 387
• Page End: 402
• Publication Date: 2017-05
• Subjects: Betti numbers -- Binomial ideal -- Lattice ideal -- Clique complex -- Square-free quadratic monomial ideal; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.06.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Let us consider the family of binomial ideals B = I + J, where J is lattice ideal and I is a square-free quadratic monomial ideal. We give a formula for calculating the Betti numbers of B . Moreover we bound the Green–Lazarsfeld invariant of a family of quadratic binomial ideals B using this formula. This result extends a previous result of Eisenbud et al. for square-free quadratic monomial ideals and extends completely Fröberg's theorem. We describe also a subfamily where we can calculate the Green–Lazarsfeld invariant of any ideal B and we also compute its first non-linear Betti number.