An algebraic proof of Iitaka's Conjecture C_{2,1}

Details An algebraic proof of Iitaka's Conjecture C_{2,1} An algebraic proof of Iitaka's Conjecture C_{2,1}

2001-03-30

arxiv.org/abs/math/0103225v1

Mathematics

Algebraic Geometry

7 pages

Scientific paper

We give a proof of Iitaka's Conjecture C_{2,1} using only elementary methods
from algebraic geometry. The main point is that, given a non-isotrivial and
relatively minimal family f : X \to B, where X is a surface and B is a curve,
both smooth and projective, we show that the direct image of the relatively
canonical sheaf has strictly positive degree.

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