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Maximally irregularly fibred surfaces of general type

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Abstract.

We generalise a method of Xiao Gang to construct ‘prototypes’ of fibred surfaces with maximal irregularity without being a product. This enables us, in the case of fibre genus g=3 to describe the possible singular fibres and to calculate the invariants of these surfaces. We also prove structure theorems on the moduli space for fibred surfaces with fibre genus g=2 and g=3.

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Authors and Affiliations

  1. Universität Essen, FB 6 (Mathematik), 45117, Essen, Germany

    Martin Möller

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  1. Martin Möller
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Correspondence to Martin Möller.

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Mathematics Subject Classification (2000): 14J10, 14J29, 14D06

Acknowledgement The author thanks his thesis advisor F. Herrlich for many stimulating discussions and a lot of patience. He also thanks E. Viehweg for worthful remarks concerning Torelli’s theorem. Some results in the same direction were obtained independently by J.-X. Cai. The author thanks him and the referee for his suggestions.

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Möller, M. Maximally irregularly fibred surfaces of general type. manuscripta math. 116, 71–92 (2005). https://doi.org/10.1007/s00229-004-0517-2

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  • DOI: https://doi.org/10.1007/s00229-004-0517-2

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