Type: Article

On the slope of relatively minimal fibrations on rational complex surfaces

Claudia R. Alcántara; Abel Castorena; Alexis G. Zamora;

Abstract:

Given a relatively minimal fibration f : S -> P(1), defined on a rational surface S, with a general fiber C of genus g, we investigate under what conditions the inequality 6(g - 1) <= K(f)(2) occurs, where K(f) is the canonical relative sheaf of f. We give sufficient conditions for having such inequality, depending on the genus and gonality of C and the number of certain exceptional curves on S. We illustrate how these results can be used for constructing fibrations with the desired property. For fibrations of genus 11 <= g <= 49 we prove the inequality: