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6. $\mathbb{G}_a$-action on the section ring


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      Problem 6.1.

      (I. Cheltsov) Let $X$ be a K-stable Fano variety, $R=R(X,-K_X)$. Does $R$ admits an action of $\mathbb{G}_a$? (For $dP_{1,2,3},$ No. For $dP_{4,5}, $ Yes). Any relation between the previous answer and $\delta, \alpha, \mathrm{vol},$ etc?

          Cite this as: AimPL: K-stability and related topics, available at http://aimpl.org/kstability.