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 $d$…

Suppose $X$ is an asymptotically conical Kähler manifold and $[b1] b5 H^{1,1}_{bd}(X,\mathbb{R})$ is a limit of $bd$-almost compactly supported Kähler classes. Then there is a func…