Abstract:Continuing a well established tradition of associating convex bodies to monomial ideals, we initiate a program to construct asymptotic Newton polyhedra from decompositions of monomial ideals. This is achieved by forming a graded family of ideals based on a given decomposition. We term these graded families powers since they generalize the notions of ordinary and symbolic powers. We introduce a novel family of irreducible powers.Irreducible powers and symbolic powers of monomial ideals are studied by means of t… Show more
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