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Canonical rings of Gorenstein stable Godeaux surfaces

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Abstract

Extending the description of canonical rings from Reid (J Fac Sci Univ Tokyo Sect IA Math 25(1):75–92, 1978) we show that every Gorenstein stable Godeaux surface with torsion of order at least 3 is smoothable.

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Acknowledgements

The results in this paper are part of our exploration of Gorenstein stable surfaces with \(K_X^2 = 1\) carried out jointly with Rita Pardini. We would like to thank her for this enjoyable collaboration. S. Rollenske enjoyed several discussions with Stephen Coughlan and Roberto Pignatelli about canonical rings in general and Godeaux surfaces in particular. We also would like to thank Giancarlo Urzúa for comments. M. Franciosi is grateful for support by the PRIN project 2010S47ARA\(\_\)011 “Geometria delle Varietà Algebriche” of italian MIUR. S. Rollenske is grateful for support by the DFG via the Emmy Noether programme and partially SFB 701.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127, Pisa, Italy

    Marco Franciosi

  2. FB 12/Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str. 6, 35032, Marburg, Germany

    Sönke Rollenske

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  1. Marco Franciosi
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  2. Sönke Rollenske
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Correspondence to Sönke Rollenske.

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Franciosi, M., Rollenske, S. Canonical rings of Gorenstein stable Godeaux surfaces. Boll Unione Mat Ital 11, 75–91 (2018). https://doi.org/10.1007/s40574-016-0114-9

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  • DOI: https://doi.org/10.1007/s40574-016-0114-9

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