Topological Triviality of Families of Singular Surfaces

Triviality of fibered Calabi-Yau manifolds without singular fibers

In this note we show that if a compact Kahler manifold with trivial canonical bundle is the total space of a holomorphic fibration without singular fibers, then the fibration is a holomorphic fiber bundle. In the algebraic case, the fibration becomes trivial after a finite base change.

奇异簇上函数芽的双李普希茨平凡性

Bi-Lipschitz triviality of function-germs on singular varieties

本文研究奇异簇上解析函数芽形变的双李普希茨平凡性，引入强有理双李普希茨平凡族概念并给出无穷小判别准则，进而得到齐次与加权齐次情形下的平凡性和刚性结果。

Whitney equisingularity of families of surfaces in $\mathbb{C}^3$

In this work, we study families of singular surfaces in $\mathbb{C}^3$ parametrized by $\mathcal{A}$-finitely determined map germs. We consider the topological triviality and Whitney equisingularity of an unfolding $F$ of a finitely determined map germ $f:(\mathbb{C}^2,0)\rightarrow(\mathbb{C}^3,0)$. We investigate the following conjecture: topological triviality implies Whitney equisingularity of the unfolding $F$? We provide a complete answer to this conjecture, given counterexamples showing how the conjecture can be false.

Generalized Levi currents and singular loci for families of plurisubharmonic functions

We show how the formalism of Levi currents on complex manifolds, as introduced by Sibony, can be used to study the analytic structure of singular sets associated to families of plurisubharmonic functions, in the sense of Slodkowski.

奇异Kähler-Einstein度量的Psh变化与光滑Kähler族的多亏格不变性

Psh variation of singular Kähler-Einstein metrics and Invariance of plurigenera for smooth Kähler families

本文证明光滑Kähler族中多重亏格维数不变性，解决Siu在2002年提出的猜想，方法涉及奇异Kähler-Einstein度量的Psh变化。

Families of distributions and Pfaff systems under duality

A singular distribution on a non-singular variety $X$ can be defined either by a subsheaf $D$ of the tangent sheaf, or by the zeros of a subsheaf $D^0$ of the sheaf of 1-forms. Although both definitions are equivalent under mild conditions on $D$, they give rise, in general, to non-equivalent notions of flat families. In this work we investigate conditions under which both notions of flat families are equivalent. In the last sections we focus on the case where the distribution is integrable, and we use our results to generalize a theorem of Cukierman and Pereira.