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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Weber, Andrzej 2016. Equivariant Hirzebruch class for singular varieties. Selecta Mathematica, Vol. 22, Issue. 3, p. 1413.


    Maxim, Laurenţiu G. and Schürmann, Jörg 2015. Characteristic Classes of Singular Toric Varieties. Communications on Pure and Applied Mathematics, Vol. 68, Issue. 12, p. 2177.


    Arapura, Donu Bakhtary, Parsa and Włodarczyk, Jarosław 2013. Weights on cohomology, invariants of singularities, and dual complexes. Mathematische Annalen, Vol. 357, Issue. 2, p. 513.


    Lunts, V. A. 2011. Categorical Resolutions, Poset Schemes, and Du Bois Singularities. International Mathematics Research Notices,


    BRASSELET, JEAN-PAUL SCHÜRMANN, JÖRG and YOKURA, SHOJI 2010. HIRZEBRUCH CLASSES AND MOTIVIC CHERN CLASSES FOR SINGULAR SPACES. Journal of Topology and Analysis, Vol. 02, Issue. 01, p. 1.


    Kovács, Sándor J. Schwede, Karl and Smith, Karen E. 2010. The canonical sheaf of Du Bois singularities. Advances in Mathematics, Vol. 224, Issue. 4, p. 1618.


    NAMIKAWA, YOSHINORI 2002. PROJECTIVITY CRITERION OF MOISHEZON SPACES AND DENSITY OF PROJECTIVE SYMPLECTIC VARIETIES. International Journal of Mathematics, Vol. 13, Issue. 02, p. 125.


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

  • SÁNDOR J. KOVÁCS (a1)
  • DOI: http://dx.doi.org/10.1023/A:1001120909269
  • Published online: 01 September 1999
Abstract

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.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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