Weighted extremal kähler metrics on resolutions of singularities

Abstract Generalizing previous results of Arezzo–Pacard–Singer, Seyyedali–Székelyhidi, and Hallam, we prove the invariance under smooth blowups of the class of weighted extremal Kähler manifolds, modulo a log‐concavity assumption on the first weight. Through recent work of Di Nezza–Jubert–Lahdili and Han–Liu, this is obtained as a consequence of a general uniform coercivity estimate for the (relative, weighted) Mabuchi energy on the blowup, which applies more generally to any equivariant resolution of singularities of Fano type of a compact Kähler klt space whose Mabuchi energy is assumed to be coercive.