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arXiv · 1602.03700

Semi-factorial nodal curves and Néron models of jacobians

Giulio Orecchia
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Abstract

A family of curves over a discrete valuation ring is called semi-factorial if every line bundle on the generic fibre extends to a line bundle on the total space. In the nodal case, 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 centered at the non-regular closed points yields a semi-factorial model of the generic fibre. As an application, we extend Raynaud's construction of the Néron (lft)-model of the jacobian of the generic fibre of a family of nodal curves to the case where the generic fibre is singular.

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Giulio Orecchia. 2016-10-24. Semi-factorial nodal curves and Néron models of jacobians. https://doi.org/10.1007/s00229-016-0895-2

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