Non-negative divisors and the Grauert metric

Grauert收缩为二次变换的负线丛的刻画

Characterization of negative line bundles whose Grauert blow-down are quadratic transforms

该研究给出了紧复空间上全纯负线丛的Grauert收缩为二次变换的充要条件，即其对偶丛的初始阶倍数丛极丰沛、高一阶倍数丛整体生成。

与负向量丛相关的奇点的不可约消歧的唯一性

Uniqueness of irreducible desingularization of singularities associated to negative vector bundles

本文证明紧复流形上负全纯向量丛经 Grauert 向下爆破所得奇点的不可约消歧唯一，并据此刻画负线丛同构及子流形到超曲面的唯一修改方式。

Kähler-Einstein metrics with mixed Poincaré and cone singularities along a normal crossing divisor

Let X be a Kähler manifold and D be a R-divisor with simple normal crossing support and coefficients between 1/2 and 1. Assuming that K_X+D is ample, we prove the existence and uniqueness of a negatively curved Kahler-Einstein metric on X\D having mixed Poincaré and cone singularities according to the coefficients of D. As an application we prove a vanishing theorem for certain holomorphic tensor fields attached to the pair (X,D).

半平面中的三个省略值与非Blaschke点除子

Three omitted values and non-Blaschke point divisors in half-planes

本研究构造了实亚纯函数反例，证明存在满足三点原像含于实轴、但半平面内非有界型且所有a-点除子不满足Blaschke条件的函数，否定了Nevanlinna1925年提出的百年悬题，核心构造由GPT-5.6 Sol Ultra自主生成。

Hermitian Metrics of Positive Holomorphic Sectional Curvature on Fibrations

The main result of this note essentially is that if the base and fibers of a compact fibration carry Hermitian metrics of positive holomorphic sectional curvature, then so does the total space of the fibration. The proof is based on the use of a warped product metric as in the work by Cheung in case of negative holomorphic sectional curvature, but differs in certain key aspects, e.g., in that it does not use the subadditivity property for holomorphic sectional curvature due to Grauert-Reckziegel and Wu.

多面体Kahler流形

Polyhedral Kahler Manifolds

在这篇文章中，我们引入了多面体Kahler流形的概念，偶数维多面体流形酉完整。我们集中在4维的情况下，证明了这样的流形是光滑的复杂的表面，并分类的度量的奇点。奇点形成一个因子，平坦联络在该因子的补数上的留数给我们一个上同调方程组。抛物型的T.望月使我们能够刻画CP ^2上具有非负曲率的多面体Kahler度量，它在复杂的线排列下具有奇点。