Reviews, developments and applications of the minimal model theorem

本文研究了代数簇和轨道上的向量丛和Higgs丛，并给出了它们的几个应用。当曲面满足一定的拓扑条件时，证明了一般型曲面上整条曲线的Green-Lang猜想的一个有效形式。我们给出了一个新的希格斯包的定义，这使我们能够构建新的希格斯包的例子。

We studied vector bundles and Higgs bundles on algebraic varieties and orbifolds, giving several applications of them. We proved an effective version of the Green-Lang conjecture for entire curves on a surface of general type when the surface satisfies a certain topological condition. We gave a new definition of Higgs bundles, which enabled us to construct new examples of Higgs bundles.