Models of Jacobians of curves
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866914799082799104 |
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| author | Holmes, David Molcho, Samouil Orecchia, Giulio Poiret, Thibault |
| author_facet | Holmes, David Molcho, Samouil Orecchia, Giulio Poiret, Thibault |
| contents | We show that the Jacobians of prestable curves over toroidal varieties always admit Néron models. These models are rarely quasi-compact or separated, but we also give a complete classification of quasi-compact separated group-models of such Jacobians. In particular we show the existence of a maximal quasi-compact separated group model, which we call the saturated model, which has the extension property for all torsion sections. The Néron model and the saturated model coincide over a Dedekind base, so the saturated model gives an alternative generalisation of the classical notion of Néron models to higher-dimensional bases; in the general case we give necessary and sufficient conditions for the Néron model and saturated model to coincide. The key result, from which most others descend, is that the logarithmic Jacobian of \cite{Molcho2018The-logarithmic} is a log Neron model of the Jacobian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_10792 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Models of Jacobians of curves Holmes, David Molcho, Samouil Orecchia, Giulio Poiret, Thibault Algebraic Geometry We show that the Jacobians of prestable curves over toroidal varieties always admit Néron models. These models are rarely quasi-compact or separated, but we also give a complete classification of quasi-compact separated group-models of such Jacobians. In particular we show the existence of a maximal quasi-compact separated group model, which we call the saturated model, which has the extension property for all torsion sections. The Néron model and the saturated model coincide over a Dedekind base, so the saturated model gives an alternative generalisation of the classical notion of Néron models to higher-dimensional bases; in the general case we give necessary and sufficient conditions for the Néron model and saturated model to coincide. The key result, from which most others descend, is that the logarithmic Jacobian of \cite{Molcho2018The-logarithmic} is a log Neron model of the Jacobian. |
| title | Models of Jacobians of curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2007.10792 |