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  • Rational, Log Canonical, Du Bois Singularities: On the Conjectures of Kollár and Steenbrink

  • SÁNDOR J. KOVÁCS
  • Journal:
    Compositio Mathematica / Volume 118 / Issue 2 / September 1999
    Published online by Cambridge University Press:
    04 December 2007, pp. 123-133
    Print publication:
    September 1999
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  • Let X be a proper complex variety with Du Bois singularities. Then H(X,C)→ H(X,${\mathcal O}$) is surjective for all i. This property makes this class of singularities behave well with regard to Kodaira type vanishing theorems. Steenbrink conjectured that rational singularities are Du Bois and Kollár conjectured that log canonical singularities are Du Bois. Kollár also conjectured that under some reasonable extra conditions Du Bois singularities are log canonical. In this article Steenbrink‘s conjecture is proved in its full generality, Kollár‘s first conjecture is proved under some extra conditions and Kollár‘s second conjecture is proved under a set of reasonable conditions, and shown that these conditions cannot be relaxed.