Betti numbers of binomial ideals. (May 2017) - de Alba, Hernán; Morales, Marcel
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.