I am looking for a reference. Let $X$ be a (complex projective) variety and $V$ some subvariety invariant under the action of a reductive group $G$. Has it been studied in general how blowing up $X$ along $V$ affects the GIT quotients of $X$ by $G$? Or anything along these lines.
2026-02-22 19:48:49.1771789729
GIT quotients under equivariant blowup
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This result can be found as Lemma 3.11 of the following article-
Partial Desingularisations of Quotients of Nonsingular Varieties and their Betti Numbers
by Kirwan.
https://www.jstor.org/stable/1971369?seq=1#metadata_info_tab_contents