复曲面簇与模形式

Imaginary quadratic points on toric varieties via universal torsors

Inspired by a paper of Salberger we give a new proof of Manin's conjecture for toric varieties over imaginary quadratic number fields by means of universal torsor parameterizations and elementary lattice point counting.

丢番图几何与复曲面簇

Diophantine geometry and toric varieties

我们提出了一些结果的投射环面品种是相关的丢番图几何。我们解释和研究几个不变量附加到这些品种的几何和组合方面。我们还给出了一个Bézout定理的Chow重量的投影品种和应用定理的连续极小。

函数域上环面簇覆叠的Campana猜想

Campana conjecture for coverings of toric varieties over function fields

本文在函数域上证明了沿边界具有高重数的射影环面簇上Campana点的Vojta abc猜想，并以此推导出函数域上射影环面簇有限覆叠的Campana猜想版本。

极值论中极核种的极值理论：全局理论

Heights on toric varieties for singular metrics: Global theory

本文提出了一种极核种的极值理论，通过凹函数积分计算极核算术品种的极值。

环面簇上有界高度的半整点

Semi-integral points of bounded height on toric varieties

本文证明了环面簇上有界高度半整点的渐近公式，并在修正首项常数后验证了光滑及部分奇异环面轨形上的Manin型猜想。

环面簇子簇上环面度量的非阿基米德Monge-Ampère测度

Non-archimedean Monge-Ampère measures for toric metrics on subvarieties of toric varieties

本文研究环面簇子簇上环面度量的非阿基米德Monge-Ampère测度，利用热带芽与热带格林函数显式描述其局部结构，推广热带相交积，为阿贝尔簇情形提供环面类比。

Strong approximation with Brauer-Manin obstruction for toric varieties

For smooth open toric varieties, we establish strong approximation off infinity with Brauer-Manin obstruction.

F1-schemes and toric varieties

This paper contains a loose collection of remarks on F1-schemes. Etale morphisms and universal coverings are introduced. The relation to toric varieties, at least for integral schemes, is clarified.In this paper it is shown that integral F1-schemes of finite type are essentially the same as toric varieties. A description of the F1-zeta function in terms of toric geometry is given. Etale morphisms and universal coverings are introduced.