Zurski之后循环多重平面的不规则性

A going-up theorem

We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.

循环矩阵半群产生的环面簇

Toric varieties from cyclic matrix semigroups

本文研究循环矩阵半群的Zariski闭包，证明其不可约分量为环面簇，并展示任意环面簇可由循环矩阵群实现，附有实例与计算说明。

Cyclic branched coverings of surfaces with abelian quotient singularities

Esnault-Viehweg developed the theory of cyclic branched coverings $\tilde X\to X$ of smooth surfaces providing a very explicit formula for the decomposition of $H^1(\tilde X,\mathbb{C})$ in terms of a resolution of the ramification locus. Later, the first author applies this to the particular case of coverings of $\mathbb{P}^2$ reducing the problem to a combination of global and local conditions on projective curves. In this paper we extend the above results in three directions: first, the theory is extended to surfaces with quotient singularities, second the ramification locus can be partiall…

单值群的Zariski稠密性：基于Picard-Lefschetz型公式

Zariski density of monodromy groups via Picard-Lefschetz type formula

本文证明沿一般位置超平面排列分支的射影空间循环覆盖万有族的单值群在相应线性群中Zariski稠密，作为Carlson-Toledo结果的退化类比，证明依赖于Picard-Lefschetz型公式。

关于纤维型曲线的拓扑：仿射结点曲线的一个扎里斯基对

On the topology of fiber-type curves: a Zariski pair of affine nodal curves

本文研究光滑射影曲面中曲线补空间基本群为循环群自由积的条件，构造无穷多纤维型曲线Zariski对，含复仿射平面内仅含结点的曲线对，证明结点位置影响射影曲线嵌入拓扑，并用有限SU(2)表示的扭曲Alexander多项式区分同阿贝尔不变量的基本群。