The dualizing sheaf on first-order deformations of toric surface singularities

Klaus Altmann, János Kollár

Research output: Contribution to journalArticlepeer-review


We explicitly describe infinitesimal deformations of cyclic quotient singularities that satisfy one of the deformation conditions introduced by Wahl, Kollár-ShepherdBarron (KSB) and Viehweg. The conclusion is that in many cases these three notions are different from each other. In particular, we see that while the KSB and the Viehweg versions of the moduli space of surfaces of general type have the same underlying reduced subscheme, their infinitesimal structures are different.

Original languageAmerican English
Pages (from-to)137-158
Number of pages22
JournalJournal fur die Reine und Angewandte Mathematik
Issue number753
StatePublished - Aug 1 2019

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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