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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.


    Illusie, Luc 2015. From Pierre Deligne’s secret garden: looking back at some of his letters. Japanese Journal of Mathematics, Vol. 10, Issue. 2, p. 237.


    Ma, Linquan 2015. $$F$$ F -injectivity and Buchsbaum singularities. Mathematische Annalen, Vol. 362, Issue. 1-2, p. 25.


    Patakfalvi, Zsolt 2015. Semi-negativity of Hodge bundles associated to Du Bois families. Journal of Pure and Applied Algebra, Vol. 219, Issue. 12, p. 5387.


    Kovács, Sándor J. 2014. Steenbrink vanishing extended. Bulletin of the Brazilian Mathematical Society, New Series, Vol. 45, Issue. 4, p. 753.


    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.


    de Fernex, Tommaso and Hacon, Christopher D. 2009. Singularities on normal varieties. Compositio Mathematica, Vol. 145, Issue. 02, p. 393.


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A simple characterization of Du Bois singularities

  • Karl Schwede (a1)
  • DOI: http://dx.doi.org/10.1112/S0010437X07003004
  • Published online: 17 July 2007
Abstract

We prove the following theorem characterizing Du Bois singularities. Suppose that $Y$ is smooth and that $X$ is a reduced closed subscheme. Let $\pi : \tilde{Y} \rightarrow Y$ be a log resolution of $X$ in $Y$ that is an isomorphism outside of $X$. If $E$ is the reduced pre-image of $X$ in $\tilde{Y}$, then $X$ has Du Bois singularities if and only if the natural map $\mathcal{O}_X \rightarrow R \pi_* \mathcal{O}_E$ is a quasi-isomorphism. We also deduce Kollár's conjecture that log canonical singularities are Du Bois in the special case of a local complete intersection and prove other results related to adjunction.

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