Crepant Property of Fujiki-Oka Resolutions for Gorenstein Abelian Quotient Singularities

Hilbert desingularizations for three dimensional canonical cyclic quotient singularities

In this paper, we shall discuss Hilbert property of ${\rm Hilb}^{G}(\mathbb{C}^{3})$, Fujiki-Oka resolutions and iterated Fujiki-Oka resolutions for three dimensional canonical cyclic quotient singularities by using the classification shown by Ishida and Iwashita\cite{II}. Finally, we shall prove that there exists a Hilbert desingularization for any three dimensional canonical cyclic quotient singularity.

Fujiki 类 $\mathcal{C}$ 中的 Monge-Ampère 退化与锥形收缩

Monge-Ampère degenerations and conifold contractions in Fujiki class $\mathcal{C}$

针对具有普通二重点奇点的 Calabi-Yau 簇，在 Fujiki 类中建立例外轨迹外的度量一致估计，并证明三维情形下度量在 Gromov-Hausdorff 意义下收敛，推广了 Song 的工作。