3 problems

Tangent-cone conjecture. At the singular point $z\in Z$, the tangent cone to $(Z,d)$ is isometric to the blowdown of the zero section in $\mathcal{O}_{\mathbb{P}(V)}(-1)$, equipped…

Let $1\leqslant k<p-1$, and let $\overline{Y}$ be the partial resolution obtained by blowing up $k$ of the lines $x=z-\zeta^jw=0$. Its isolated singularity is modeled by … Let $d$…

Let $(X,d_\infty)$ be a Gromov–Hausdorff limit as in the construction of Donaldson and Sun, let $x\in X$ be a point, let $C=C_xX$ be a metric tangent cone, and let $W$ be the affin…