TITLE: Recent ideas in Macaulayfication?
QUESTION [7 upvotes]: Kawasaki has shown that a quasi-projective variety over a field has a Macaulayfication.  His construction does not preserve the Cohen-Macaulay locus of the original variety, only a finite set of points in the Cohen-Macaulay locus.  Have there been any recent improvements of Kawasaki's result that give Macaulayfications that preserve the entire Cohen-Macaulay locus of the original variety?

REPLY [2 votes]: Regarding Gorensteinification, it is possible to start with a demi-normal (ie, G_1, S_2, and seminormal) quasi-projective variety U and find a demi-normal projective closure.  This is not really a Gorensteinification, but something close to normalization without completely normalizing a given projective closure of U.  Also, for Q-Gorenstein varieties at least, the cyclic covering lemma with Cohen-Macaulayfication would probably do the trick.