, Volume 84, Issue 1, pp 225-244

On the invariants of base changes of pencils of curves, I

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The main purpose of this paper is to prove the nonnegativity of the basic invariants of base changes of a surface fibration, which is conjectured by Xiao Gang. For this purpose we obtain some new inequalities between the invariants of the singularities ofz d =f(x, y).

This work is supported by the National Natural Science Foundation of China and by the Science Foundation of the University Doctoral Program of CNEC. This paper is corrected while the author is visiting Max-Planck-Institut für Mathematik in Bonn.