2 problems

Let $V$ be a Fano orbifold, meaning a compact Kähler orbifold whose Ricci-form cohomology class is represented by a positive $(1,1)$-form. In the quasi-regular setting, $V$ is the…

Nakagawa's conjecture. If the Futaki invariant of $X$ vanishes, then $X$ admits a Kähler–Einstein metric, and its automorphism group is reductive.