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/9901128
2 pages; Latex
arxiv created 1999/01/27 · arxiv updated 2009/11/30
Let f:S ->B be a relatively minimal fibred surface. In this note we give a partial affirmative answer to a conjecture of Xiao, proving that the direct image of the relative dualizing sheaf of f is ample when the slope of the fibration is less than 4, if the general fibre of f is non-hyperelliptic or the genus of the fibre or of the base curve is low.