The Minkowski Equality of Big Divisors

On the structure of a log smooth pair in the equality case of the Bogomolov-Gieseker inequality

We study the structure of a log smooth pair when the equality holds in the Bogomolov-Gieseker inequality for the logarithmic tangent bundle and this bundle is semistable with respect to some ample divisor. We also study the case of the canonical extension sheaf.

满足宫冈等式的极小射影簇

Minimal projective varieties satisfying Miyaoka's equality

本文针对满足宫冈等式的极小射影klt簇建立结构定理，证明其典范除子半充足且小平维数为0/1/2，明确极大拟平展覆盖与饭纤维化结构，并将结果推广至有nef反典范除子的射影klt簇。

因子体积的可微性与Teissier问题

Differentiability of volumes of divisors and a problem of Teissier

本文给出了Boucksom，Demailly，Paun和Peternell首次引入的伪有效类的正积的代数构造，并利用它们证明了投射簇的Neron-Severi空间上的体积函数是（一次）可微的.微分表示为一个积极的产品，我们还将其与Ein等人和高山介绍的限制卷。然后，我们应用我们的可微性结果证明了代数几何版本的凸几何中的不等式，使我们能够表征的平等情况下的Khovanskii-Teissier不等式的nef和大类。

Surfaces close to the Severi lines

Let $X$ be a surface of general type with maximal Albanese dimension: if $K_X^2<\frac{9}{2}χ(\mathcal{O}_X)$, one has $K_X^2\geq 4χ(\mathcal{O}_X)+4(q-2)$. We give a complete classification of surfaces for which equality holds for $q(X)\geq 3$: these are surfaces whose canonical model is a double cover of a product elliptic surface branched over an ample divisor with at most negligible singularities which intersects the elliptic fibre twice. We also prove, in the same hypothesis, that a surface $X$ with $K_X^2\neq 4χ(\mathcal{O}_X)+4(q-2)$ satisfies $K_X^2\geq 4χ(\mathcal{O}_X)+8(q-2)$ and we …

可接受的HYM度量在klt KE变种上的应用以及大反canonical K稳定变种的MY等式

Admissible HYM metrics on klt KE varieties and the MY equality for big anticanonical K-stable varieties

本文研究了Kähler-Einstein变种上反射sheaf的稳定性、K稳定变种的Miyaoka-Yau不等式等式以及holomorphic向量包的semistability性质。

曲线上任意次外部张量积的一般无穷小 Newton-Okounkov 体的 Minkowski 分解

Minkowski Decompositions for Generic Infinitesimal Newton-Okounkov Bodies of Arbitrary-Degree External Tensor Products on Products of Curves

本文给出光滑射影曲线乘积上正次外部张量积的无穷小 Newton-Okounkov 体的显式 Minkowski 分解公式，并据此得到 Minkowski 包含取等的精确判据及有限多个体在共同很一般轨迹上的实现。

除子类群秩一的环状奇点的非交换凝聚解消

Non-commutative crepant resolutions of toric singularities with divisor class group of rank one

本文证明并分类了除子类群秩一的Gorenstein环状奇点的环状非交换凝聚解消（NCCR），通过上集与Iyama-Wemyss突变建立导出等价，并在非金字塔情形下给出二聚体模型实现。

Nef和大类的Kobayashi-Hitchin对应

The Kobayashi-Hitchin correspondence for nef and big classes

通过引入适应闭正(1,1)-流和适应Hermitian-Yang-Mills度量的概念，建立了nef和大上同调类的Kobayashi-Hitchin对应，并应用于Bogomolov-Gieseker不等式和Miyaoka-Yau不等式的等式情形。