Slope inequalities for fibred surfaces via GIT

Details Slope inequalities for fibred surfaces via GIT Slope inequalities for fibred surfaces via GIT

2004-11-29

arxiv.org/abs/math/0411639v3

Osaka Journal of Mathematics, Vol. 45, No. 4 (2008)

Mathematics

Algebraic Geometry

13 pages, revised version

Scientific paper

In this paper we present a generalisation of a theorem due to Cornalba and Harris, which is an application of Geometric Invariant Theory to the study of invariants of fibrations. In particular, our generalisation makes it possible to treat the problem of bounding the invariants of general fibred surfaces. As a first application, we give a new proof of the slope inequality and of a bound for the invariants associated to double cover fibrations.

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