Classification of can-Var diagrams of mixed Hodge structures and monodromic mixed Hodge modules on $\mathbb{C}$

Source abstract

By our previous work, the category of unipotent monodromic mixed Hodge modules on $\mathbb{C}$ is equivalent to the category of can-Var diagrams of mixed Hodge structures. In this paper, we show that the associated graded diagram with respect to the weight filtrations decomposes as a finite direct sum of four basic types tensored with pure Hodge structures, which we call a split graded model. We then show that every unipotent monodromic mixed Hodge module is represented by a split graded model together with a finite family of $\mathbb{C}$-linear maps. We also obtain an analogous description in the case where the monodromy has no eigenvalue $1$.