Convex bodies and asymptotic invariants for powers of monomial ideals
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. Asymptotic invariants for these graded families are expressed as solutions to linear optimization problems on the respective convex bodies. This allows to establish a lower bound on the Waldschmidt constant of a monomial ideal by means of a more easily computable invariant, which we introduce under the name of naive Waldschmidt constant.
Keywords
Cite
@article{arxiv.2101.04008,
title = {Convex bodies and asymptotic invariants for powers of monomial ideals},
author = {João Camarneiro and Benjamin Drabkin and Duarte Fragoso and William Frendreiss and Daniel Hoffman and Alexandra Seceleanu and Tingting Tang and Sewon Yang},
journal= {arXiv preprint arXiv:2101.04008},
year = {2022}
}
Comments
final version - to appear in the Journal of Pure and Applied Algebra