We characterize the strongly Cohen–Macaulay ideals of second analytic deviation one in terms of depth properties of the powers of the ideal in the ‘standard range.’ This provides an explanation of the behaviour of certain ideals that have appeared in the literature.

We prove a generalization of Demailly-Ein-Lazarsfeld’s subadditivity formula [DEL] and Mustaţǎ’s summation formula [Mu] for multiplier ideals to the case of singular varieties, using characteristic p methods. As an application of our formula, we improve Hochster-Huneke’s result [HH4] on the growth of symbolic powers of ideals in singular affine algebras.

Continuing a well established tradition of associating convex bodies to monomial ideals, we initiate program construct asymptotic Newton polyhedra from decompositions ideals. This is achieved by forming graded family ideals based on given decomposition. We term these families powers since they generalize the notions ordinary and symbolic powers. Asymptotic invariants for are expressed as soluti...

We describe some of the determinantal ideals attached to symmetric, exterior and tensor powers of a matrix. The methods employed use elements of Zariski's theory of complete ideals and of representation theory. Let R be a commutative ring. The determinantal ideals attached to matrices with entries in R play ubiquitous roles in the study of the syzygies of R{modules. In this note, we describe so...