A procedure for computing the log canonical threshold of a binomial ideal

TL;DR

This paper introduces a method to compute the log canonical threshold of binomial and monomial ideals by reducing the problem to a minimum of a specific function, leveraging the structure of fans based on exponents.

Contribution

It provides a novel procedure that simplifies the calculation of log canonical thresholds for binomial ideals using geometric and combinatorial tools.

Findings

The computation reduces to a minimization problem of a function.

The minimum is attained at a ray of a fan determined by exponents.

The method applies to arbitrary binomial and monomial ideals.

Abstract

We present a procedure for computing the log-canonical threshold of an arbitrary ideal generated by binomials and monomials. The computation of the log canonical threshold is reduced to the problem of computing the minimum of a function, which is defined in terms of the generators of the ideal. The minimum of this function is attained at some ray of a fan which only depends on the exponents of the monomials appearing in the generators of the ideal.