Postdoc Bojie He，Peking University

In these series of talks, we will focus on the study of the Iitaka conjecture, which predicts the subadditivity of Kodaira dimensions for any algebraic fiber space. In the first part, we recall some basic results in the study of Iitaka conjecture and then give an analytic approach to O. Fujino’s result on the subadditivity of the log Kodaira dimensions. In the second part, we introduce the notion of generalized numerical Kodaira dimension with multiplier ideal sheaf and establish subadditive inequalities in terms of this notion. We also recall the definition of generalized Kodaira dimension with multiplier ideal sheaf and then study the Newton-Okounkov body associated to its corresponding graded subalgebra. As an application, we give another proof of Zhou-Zhu’s subadditivity formula of generalized Kodaira dimensions, in the special case when the singular metric with semi-positive curvature current has inf-analytic singularities, by using generalized Iitaka fiberings. This is joint work with Prof. Xiangyu Zhou.