4 problems

Let $(X,L)$ be a smooth polarized manifold, where $c_1(L)$ denotes the first Chern class of $L$, and let K-polystability mean that every test configuration has nonnegative Donaldso…

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 $(X,B;L)$ be a polarized pair, and let $\sigma_{\mathrm{div}}(X,B;L)$ and $\sigma_{\mathrm{K}}(X,B;L)$ denote the divisorial and K-stability thresholds, respectively. Threshold…

Let $(X,L)$ be a smooth projective variety over a number field $K$. Semistable arithmetic Yau–Tian–Donaldson conjecture. The following conditions are equivalent:…