\(F\)-pure thresholds of homogeneous polynomials (Q274128)

The authors study the \(F\)-pure thresholds of polynomials that are homogeneous under some \(\mathbb{N}\)-grading with an isolated singularity at the origin. The main result, Theorem 3.5, gives a finite list of possible values of the \(F\)-pure thresholds of such polynomials, and in many cases it gives the exact values. The main result is an extention of the methods and results of \textit{B. Bhatt} and \textit{A. K. Singh} [Math. Ann. 362, No. 1--2, 551--567 (2015; Zbl 1328.13006)]. As applications, the authors obtain results on uniform bounds for the difference between log canonical and \(F\)-pure thresholds, and results on the ACC conjecture for \(F\)-pure thresholds, and for homogeneous polynomials with isolated singularities.