6 problems

Let $X$ be a polarized variety with polarization $L_X$, let $D$ be a divisor, and fix a cone angle along $D$. A cscK cone metric is a Kähler cone metric on $(X,D)$ with constant sc…

Let $X$ be a polarized variety with polarization $L_X$, and let $D$ be a divisor. Suppose that $D$ admits a constant-scalar-curvature Kähler metric with nonpositive scalar curvatur…

Let $X$ be a compact complex manifold, let $L\to X$ be an ample line bundle, let $D$ be a divisor on $X$, and let $\beta$ determine a cone angle $2\pi\beta$ along $D$. Write…

The cscK cone metric and log-K-polystability conjecture. The following three conditions are equivalent: (i) $X$ admits a cscK cone metric along $\mathcal{D}$ in any ample class

Log Donaldson–Tian–Yau conjecture. $((X,D);L)$ is log $K$-polystable with cone angle $2\pi\beta$ if and only if $X$ admits a cscK metric in $c_1(L)$ with cone singularities along…

Let $(X,Y)$ be a pair consisting of a compact Kähler manifold $X$ and a divisor $Y$, and let $(X,Y)$ be log-K-stable in the logarithmic sense. A constant scalar curvature conic Käh…