Abstract

Given a fibration f: X -> Z, a natural question is how we can relate the Kodaira dimensions of X, Z, and the fibres. The Iitaka conjecture addresses this problem. In characteristic 0, it is proven in many cases, while it is known to not hold in general in positive characteristics. Recently, a similar statement for the anticanonical divisors was proven in characteristic 0. The same results can be extended also to positive characteristics in low dimensions. At the end, we will see also some counterexamples constructed from Tango-Raynaud surfaces.

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