Bounded deformations of (ε, δ) -log canonical singularities

Jingjun Han, Jihao Liu, Joaquin Moraga

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In this paper we study (ε,δ)-lc singularites, i.e. ε-lc singularities admitting a δ-plt blow-up. We prove that n-dimensional (ε,δ)-lc singularities are bounded up to a deformation, and 2-dimensional (ε,δ)-lc singularities form a bounded family. Furthermore, we give an example which shows that (ε,δ)-lc singularities are not bounded in higher dimensions, even in the analytic sense.

Original languageEnglish (US)
Pages (from-to)1-28
Number of pages28
JournalJournal of Mathematical Sciences (Japan)
Issue number1
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Bounded families
  • Deformations
  • Klt singularities
  • Log discrepancies
  • Plt blow-up


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