Center conditions: Rigidity of logarithmic differential equations

函子单项式化与相对主元化中中心的唯一性

Functorial monomialization and uniqueness of centers for relative principalization

本文研究相对对数情形下理想主元化的函子性问题，证明本征映射中Kummer与加权对数中心均可函子式单项式化，从而得到群作用等变且与基局部化相容的特征0相对主元化与对数光滑约化。

Degree of logarithmic foliations of type (1,1,1)

The space of codimension one holomorphic foliations of degree 1 in a projective space has an irreducible component whose general element is a logarithmic differential 1-form with simple poles in three hyperplanes. We compute its projective degree by resolving its rational parametrization map through succesive blow-ups with smooth centers.

高次对数几何中的形变理论

On Deformation Theory in Higher Logarithmic Geometry

本文在高次对数几何中引入形变理论，通过重新概念化精确化过程并构造精确化切丛，得到对数余切复形，应用于刻画平方零扩张与étale刚性。

Smooth points of the space of plane foliations with a center

We prove that a logarithmic foliation corresponding to a generic line arrangement of $d+1 \geq 3$ lines in the complex plane, with pairwise natural and co-prime residues, is a smooth point of the center set of plane foliations (vector fields) of degree $d$.

高维对数 Riemann--Hurwitz 不等式与覆盖的刚性

A Higher dimensional log Riemann--Hurwitz inequality and rigidity of covers

本文证明了对数 Riemann--Hurwitz 不等式及其严格版本，并应用于曲线模空间，得出带层级结构的模空间的有限满射自态射必为同构。

配置空间之间映射的刚性

Rigidity of maps between configuration spaces

研究辫群同态\(\Phi\colon\mathrm{B}_n\to\mathrm{B}_m\)（\(n\geq5\)，\(m\geq3\)），在特定条件下证明\(m = n\)且\(\Phi\)与模中心的自同构一致，还证明相关全纯映射的性质，解决了一些猜想和问题。