Iitaka-Viehweg conjectures C and C++

Abstract

Given a fibre space $X/S$ with the generic geometric fibre of Kodaira dimension $\ge 0$, we shall construct a variety $Y$ ramified over $X$ along such a horizontal hyperplane with respect to $X/S$ that Kollár and Kawamata had proved Viehweg conjecture for $Y/S$ with the generic geometric fibre of general type or of the abundant canonical invertible sheaf where Viehweg dimensions of $X/S$ and $Y/S$ are equal, respectively. We shall show that Viehweg dimension of $X/S$ is not greater than that of $Y/S$ by Mochizuki's Galois theory.

References in corpus (2)

• Algebraic (geometric) $n$-stacks
• A closed model structure for $n$-categories, internal $Hom$, $n$-stacks and generalized Seifert-Van Kampen