在双有理几何的极小模型纲领里，富余猜想是其中最重要的猜想之一。在对数典范对的范畴下，富余猜想的一个等价猜想是有限生成猜想。本研究拟通过用半对数典范平凡纤维化以及混合霍奇理论相结合的方法，证明在低小平维数下对数典范环的有限生成性。

In the minimal model program of birational geometry, abundance conjecture is one of the most important conjectures. In the framework of log canonical pairs, abundance conjecture is equivalent to finite generation conjecture. In this research, we try to prove finite generation conjecture with lower Kodaira dimensions by using the slc-trivial fibration and the mixed Hodge theory.