Abstract
In this article, we study specializations of multigradings and apply them to the problem of the computation of the arithmetical rank of a lattice ideal I L 𝒢 ⊂ K[x 1,…, x n ]. The arithmetical rank of I L 𝒢 equals the ℱ-homogeneous arithmetical rank of I L 𝒢 , for an appropriate specialization ℱ of 𝒢. To the lattice ideal I L 𝒢 and every specialization ℱ of 𝒢, we associate a simplicial complex. We prove that combinatorial invariants of the simplicial complex provide lower bounds for the ℱ-homogeneous arithmetical rank of I L 𝒢 .
ACKNOWLEDGMENT
The authors thank the referee for his careful reading of the manuscript and his helpful remarks.
Notes
Communicated by R. Villarreal.