Regular sequences on squares of monomial ideals

Abstract

We use initially regular sequences that consist of linear sums to explore the depth of $$R/I^2$$ , when I is a monomial ideal in a polynomial ring R. We give conditions under which these linear sums form regular or initially regular sequences on $$R/I^2$$ . We then obtain a criterion for when $${{\,\mathrm{depth}\,}}R/I^2>1$$ and a lower bound on $${{\,\mathrm{depth}\,}}R/I^2$$ .