A boundedness conjecture for minimal log discrepancies on a fixed germ

Abstract

We consider the following conjecture: on a klt germ (X,x), for every finite set I there is a positive integer N with the property that for every R-ideal J on X with exponents in I, there is a divisor E over X that computes the minimal log discrepancy of (X,J) at x and such that its discrepancy k_E is bounded above by N. We show that this implies Shokurov's ACC conjecture for minimal log discrepancies on a fixed klt germ and give some partial results towards the conjecture.

This version is substantially different from the first version of the paper

References in corpus (4)

• Which powers of holomorphic functions are integrable?
• On minimal log discrepancies on varieties with fixed Gorenstein index
• Contact loci in arc spaces
• On semi-continuity problems for minimal log discrepancies

Cited by in corpus (2)

• Birational boundedness of rationally connected Calabi-Yau 3-folds
• Surfaces containing two isotropic circles through each point