Depth and regularity modulo a principal ideal

Abstract

We study the relationship between depth and regularity of a homogeneous ideal I and those of (I,f) and I:f, where f is a linear form or a monomial. Our results has several interesting consequences on depth and regularity of edge ideals of hypegraphs and of powers of ideals.

20 pages, published version, Journal of Algebraic Combinatorics 2018