On the slope of relatively minimal fibrations on rational complex surfaces

• Autores: Claudia R. Alcántara, Abel Castorena, A.G. Zamora
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 62, Fasc. 1, 2011, págs. 1-15
• Idioma: inglés
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• Resumen

  • Given a relatively minimal fibration {f:S \to \mathbb{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)\le 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:

    6(g-1) +4 -4\sqrt g \le K_f^2.