Jacobians的Néron模型存在的一个判据
A criterion for existence of Néron models of jacobians
摘要：
如果基$S$的维数大于1，则阿贝尔簇的Néron模型不一定存在。我们引入了一个新的条件，所谓的复曲面的可加性，在一个正规交叉因子$D\subset S$的节点减少的平滑曲线的家庭。该条件是必要的和充分的存在一个Néron模型的雅可比的家庭;它只取决于贝蒂数的对偶图的纤维的家庭，或环面秩的纤维的雅可比。
英文摘要：
Néron models of abelian varieties do not necessarily exist if the base $S$ has dimension higher than 1. We introduce a new condition, called toric additivity, on a family of smooth curves having nodal reduction over a normal crossing divisor $D\subset S$. The condition is necessary and sufficient for existence of a Néron model of the jacobian of the family; it depends only on the Betti numbers of the dual graphs of the fibres of the family, or on the toric ranks of the fibres of the jacobian.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
