Slope inequalities for fibred surfaces via GIT

Lidia Stoppino

doi:ojm/1227708831

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Home > Journals > Osaka J. Math. > Volume 45 > Issue 4 > Article

December 2008 Slope inequalities for fibred surfaces via GIT

Lidia Stoppino

Osaka J. Math. 45(4): 1027-1041 (December 2008).

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Abstract

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.