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 $d$…

Donaldson–Sun's algebraicity conjecture. Both $M$ and $C$ depend only on the underlying algebraic structure of the germ $x\in X_\infty$. The conjecture concerns the algebraicity an…