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On the slope of fibred surfaces

Published online by Cambridge University Press:  22 January 2016

Miguel Ángel Barja  and
Francesco Zucconi
Miguel Ángel Barja
Affiliation:
Departament de Matmática Aplicada I, Universitat Politécnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain, barja@ma1.upc.es
Francesco Zucconi
Affiliation:
Departament de Matmática Aplicada I, Universitat Politécnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain, barja@ma1.upc.es
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Abstract

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We give an asymptotically sharp lower bound for the slope λ(f) of a fibration f : S → B, where S is a surface and B is a curve, if there exists an involution on the general fibre F of f. We also construct a new lower bound of λ(f) depending increasingly on the irregularity of S; as an application of this new bound we have a criteria to control the existence of other fibrations on S.

Keywords

14H1014J10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 164 , December 2001 , pp. 103 - 131
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

References

[1] Barja, M. A., On the slope of bielliptic fibrations, to appear in the Proc. of the A.M.S. Google Scholar
[2] Barja, M. A., On the slope and geography of fibred surfaces and threefolds, Ph. D. Thesis. University of Barcelona, 1998.Google Scholar
[3] Barja, M. A. and Naranjo, J.C., Extension of maps defined on many fibres, Collect Math., 49, 2-3 (1998), 227-238.Google Scholar
[4] Beauville, A., L’application canonique pour les surfaces pour les surfaces de type général, Invent. Math., 55 (1979), 121-140.Google Scholar
[5] Beauville, A., Annullation du H1 et systèmes paracanoniques sur les surfaces, J. Reine Math., 388 (1988), 149-157.Google Scholar
[6] Catanese, F., Fibred surfaces, varieties isogenous to a product and related moduli spaces, to appear American Journal Math, 1–42.Google Scholar
[7] Chen, Z., On the bound of the slope of a non-hyperelliptic fibration of genus 4, Intern. J. Math.,, 4, No.3 (1993), 367–378.Google Scholar
[8] Fujita, T., On Kaehler fibre spaces over curves, J. Math. Soc. Japan, 30 (1978), 779–794.Google Scholar
[9] Harder, G. and Narasimhan, M. S., On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann., 212 (1974), 215–248.Google Scholar
[10] Konno, K., On the irregularity of special non-canonical surfaces, Publ. Res. Inst. Math. Sci., 30 (1994), 671–688.CrossRefGoogle Scholar
[11] Konno, K., A lower bound of the slope of trigonal fibrations, Internat. J. Math., 7 no. 1 (1996), 19–27.Google Scholar
[12] Konno, K., A note on a question by M.A. Barja, personal communication (1997).Google Scholar
[13] Konno, K., Clifford index and the slope of fibred surfaces, J. Algebraic Geom., 8 no.2 (1999), 207–220.Google Scholar
[14] Nakayama, N., Zariski decomposition problem for pseudo effective divisors, Proceedings of the meeting and the workshop “Algebraic Geometry and Hodge Theory”, vol I, Hokkaido University Math. preprint series.Google Scholar
[15] Pirola, G., On a conjecture of Xiao, J. Reine angew. Math., 431 (1992), 75-89.Google Scholar
[16] Stankova-Frenkel, Z.E., Moduli of trigonal curves, Preprint (1997).Google Scholar
[17] Xiao, G., fibred algebraic surfaces with low slope, Math. Ann., 276 (1987), 449–466.Google Scholar
[18] Xiao, G., Irregularity of surfaces with a linear pencil, Duke Math. J., 55, no. 3 (1987), 597–602.Google Scholar