Английская Википедия:Du Bois singularity

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In algebraic geometry, Du Bois singularities are singularities of complex varieties studied by Шаблон:Harvtxt.

Шаблон:Harvtxt gave the following characterisation of Du Bois singularities. Suppose that <math>X</math> is a reduced closed subscheme of a smooth scheme <math>Y</math>.

Take a log resolution <math>\pi: Z \to Y</math> of <math>X</math> in <math>Y</math> that is an isomorphism outside <math>X</math>, and let <math>E</math> be the reduced preimage of <math>X</math> in <math>Z</math>. Then <math>X</math> has Du Bois singularities if and only if the induced map <math>\mathcal{O}_X \to R\pi_{*}\mathcal{O}_E</math> is a quasi-isomorphism.

References


Шаблон:Algebraic-geometry-stub