本项目研究的对象代数曲面纤维化是代数几何中一个重要的研究分支，并且是研究代数曲面的性质和代数曲线模空间的几何的重要工具。项目的主要目标是研究代数曲面纤维化中的重要不变量斜率的下界与曲面纤维化的几何性质之间的关系，着重研究斜率的下界与纤维化霍奇丛的正性以及一般纤维的几何特性之间的关系，同时将其应用于Arakelov不等式和代数曲面的地理学等问题的研究上，推进或解决一些公开问题。本项目的预期成果将会在数学领域高水平期刊发表，并且对代数曲面纤维化的研究有积极推动作用。

This project is going to study the surface fibration, which is not only one of the significant branches in algebraic geometry, but also provides an important tool in the study of algebraic surfaces and the moduli of algebraic curves. The slope is an important invariant for a surface fibration. The main goal in this project is to study the relation of the lower bound of the slope with the geometrical properties of the surface fibrations. Especially, we plan to study the relations of the lower bound of the slope with the positivity of the Hodge bundle of the fibrations and with the geometrical properties of the general fibers. Meanwhile, we will also apply it to the study of Arakelov inequalities and the geography of algebraic surfaces, and make some progress or solve some open questions in these areas. We expect to publish our results on the mathematical journals of high level, and hope to play an active role in promoting the study of the fibrations of algebraic surfaces.