Year: 2022
Type: article
Abstract: We work with a smooth relative curve $X_U/U$ with nodal reduction over an excellent and locally factorial scheme $S$. We show that blowing up a nodal model of $X_U$ in the ideal sheaf of a section yields a new nodal model, and describe how these models relate to each other. We construct a N\'eron model for the Jacobian of $X_U$, and describe it locally on $S$ as a quotient of the Picard space of a well-chosen nodal model. We provide a combinatorial criterion for the N\'eron model to be separated. Comment: 37 pages including bibliography. Comments are welcome. To appear in \'Epijournal de G\'eom\'etrie Alg\'ebrique, Volume 6 (2022), Article No. 17
Author: Thibault Poiret
Institution: Leiden University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W3139012606