ACC for Minimal Log Discrepancies of Exceptional Singularities

By Jingjun Han, Jihao Liu, V. Shokurov. Peking Mathematical Journal, 2019

77 citations recorded by the source corpus.

In this paper, we study the ascending chain condition (ACC) conjecture for minimal log discrepancies (mlds), proposed by the third author. We show the ACC conjecture holds for singularities admitting ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-plt blow-ups. In particular, this gives the ACC for mlds for exceptional singularities. The key ingredients in the proofs of our main results are the Birkar–Borisov–Alexeev–Borisov theorem, proved by Birkar, the boundedness of complements conjecture for arbitrary DCC coefficients, proposed by the third author and proved in this paper, and the existence of uniform R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}$$\end{document}-complementary rational polytopes.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c1cb85a7ae2e1ab013e3a9a310157de0c80495b6

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In Algebra and Number Theory

  1. Yuchen Liu
  2. H. Blum

In Geometry and Topology

  1. H. Blum
  2. Yuchen Liu
  3. Chi Li
  4. Chenyang Xu
  5. Ziquan Zhuang
  6. Mattias Jonsson
  7. Kento Fujita
  8. Xiaowei Wang

In Mathematical Physics

  1. Yuchen Liu
  2. H. Blum

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