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On the Slope of Fibred Surfaces

1999/01/27 by Miguel A. Barja, Barja, Miguel A., Francesco Zucconi +1
Mathematics · #14H10 #14J10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H10 #msc:14J10

paper · pdf · doi:10.48550/arxiv.math/9901129

29 pages: Latex

arxiv created 1999/01/27 · arxiv updated 2009/11/30

Abstract

Given a relatively minimal non locally trivial fibred surface f: S->B, the slope of the fibration is a numerical invariant associated to the fibration. In this paper we explore how properties of the general fibre of f and global properties of S influence on the lower bound of the slope. First of all we obtain lower bounds of the slope when the general fibre is a double cover. We also obtain a lower bound depending as an increasing function on the relative irregularity of the fibration, extending previous results of Xiao. We construct several families of examples to check the assimptotical sharpness of our bounds.

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