Abstract
Following Pépin, we call a family of curves over a discrete valuation ring semi-factorial if every line bundle on the generic fibre extends to a line bundle on the total space. In the case of nodal curves with split singularities, we give a sufficient and necessary condition for semi-factoriality, in terms of combinatorics of the dual graph of the special fibre. In particular, we show that performing one blow-up with center the non-regular closed points yields a semi-factorial model of the generic fibre. As an application, we extend the result of Raynaud relating Néron models of smooth curves and Picard functors of their regular models to the case of (possibly singular) curves having a semi-factorial model.
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01 September 2017
An erratum to this article has been published.
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An erratum to this article is available at https://doi.org/10.1007/s00229-017-0968-x.
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Orecchia, G. Semi-factorial nodal curves and Néron models of jacobians. manuscripta math. 154, 309–341 (2017). https://doi.org/10.1007/s00229-016-0895-2
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DOI: https://doi.org/10.1007/s00229-016-0895-2