Talk:Rational singularity

Normality

"Alternately, one can remove the normality hypothesis on X"

In this alternate version, does the condition imply that X is normal? Or is this a proper extension of the concept? It would be nice if the page made this clear one way or the other. 128.178.94.133 (talk) 08:09, 25 September 2008 (UTC)

This is not really a "removal of the normality hypothesis". The derived category condition implies that ${\mathcal {O}}_{X}\rightarrow f_{*}{\mathcal {O}}_{Y}$ is an isomorphism (of sheaves). This implies that $X$ is normal.