Iitaka-Viehweg conjectures C and C++

Details Iitaka-Viehweg conjectures C and C++ Iitaka-Viehweg conjectures C and C++

2009-10-04

arxiv.org/abs/0910.0604v3

Mathematics

Algebraic Geometry

Scientific paper

Given a fibre space $X/S$ with the generic geometric fibre of Kodaira dimension $\geq 0$, we shall construct a variety $Y$ ramified over $X$ along such a horizontal hyperplane with respect to $X/S$ that Koll\'ar 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.

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