环簇上的双曲线法

Pluripotential theory for tropical toric varieties and non-archimedean Monge-Ampére equations

Tropical toric varieties are partial compactifications of finite dimensional real vector spaces associated with rational polyhedral fans. We introduce plurisubharmonic functions and a Bedford--Taylor product for Lagerberg currents on open subsets of a tropical toric variety. The resulting tropical toric pluripotential theory provides the link to give a canonical correspondence between complex and non-archimedean pluripotential theories of invariant plurisubharmonic functions on toric varieties. We will apply this correspondence to solve invariant non-archimedean Monge--Ampère equations on tori…

Manin's conjecture on toric varieties with different heights

In this paper I verify Manin's conjecture for a class of rational projective toric varieties with a large class of heights other than the usual one that comes from the standard metric on projective space.

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.

Diophantine geometry and toric varieties

We present some results on projective toric varieties which are relevant in Diophantine geometry. We interpret and study several invariants attached to these varieties in geometrical and combinatorial terms. We also give a Bézout theorem for the Chow weights of projective varieties and an application to the theorem of successive minima.

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。

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.