5 problems

Li's normalized-volume conjecture for the exceptional weighted valuation. For all other cases of $(n,k)$, ${\widehat{\rm vol}}$ should be minimized at the valuation associated to t…

Let $(M,\omega)$ be a compact Kähler manifold of complex dimension $m$ such that $[\omega]=2\pi c_1(M)$, $\operatorname{Ric}(\omega)\ge R_0>0$, and…

Let $X$ be a compact Fano manifold, and let a nontrivial holomorphic vector field mean a holomorphic vector field on $X$ that is not identically zero. Kähler-Einstein existence con…

Let $(X,D)$ be a log canonical pair with $K_X+D$ ample. Write $X_0=X_{\mathrm{reg}}\setminus\operatorname{Supp}(D)$, and let … where $\mathscr I(X,D)$ is the multiplier ideal attac…

Let $M$ be a Fano manifold and let $D$ be a smooth anti-canonical divisor. By the cited result, there is a complete Calabi–Yau metric on $M\setminus D$. For $0<\beta\leq 1$, let a…