A boundedness conjecture for minimal log discrepancies on a fixed germ

@article{Musta2015ABC,
  title={A boundedness conjecture for minimal log discrepancies on a fixed germ},
  author={Mircea Mustaţǎ and Yusuke Nakamura},
  journal={arXiv: Algebraic Geometry},
  year={2015}
}
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. 
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