Local and Global Methods in Algebraic Geometry

By M. Mustaţă, Yusuke Nakamura. Contemporary Mathematics, 2015

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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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Geometry and Topology

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