Smoothing of Limit Linear Series on Curves and Metrized Complexes of Pseudocompact Type
Smoothing of Limit Linear Series on Curves and Metrized Complexes of Pseudocompact Type
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曲线上极限线性级数的平滑和伪紧型度量复形
DOI：
10.4153/s0008414x18000068
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Xiang He
中科院分区：
文献类型：
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作者：
Xiang He
摘要利用同类型曲线上的前极限线性序列的概念，研究了Osserman极限序列（拟紧型曲线上）与Amini-Baker极限线性序列（具有相应下曲线的度量复合体上）之间的联系。然后，应用Osserman极限线性序列的光滑性定理，我们推导出，对于某些度量配合物，或对于某些类型的Amini-Baker极限线性序列，其光滑性等价于某种“弱粘接条件”。对于任意度量的伪紧型配合物，弱胶合条件（当它适用时）也是光滑性的必要条件。作为应用，我们证实了与某正则平滑族相关的度量图上特定因子的提升性，并给出了carcaright、Jensen和Payne关于避顶点因子的新证明，并将其推广到秩1的因子上，即对于度量图，相邻的任意一对顶点之间最多可以有三条边（而不是两条）。
Abstract We investigate the connection between Osserman limit series (on curves of pseudocompact type) and Amini–Baker limit linear series (on metrized complexes with corresponding underlying curve) via a notion of pre-limit linear series on curves of the same type. Then, applying the smoothing theorems of Osserman limit linear series, we deduce that, fixing certain metrized complexes, or for certain types of Amini–Baker limit linear series, the smoothability is equivalent to a certain “weak glueing condition”. Also for arbitrary metrized complexes of pseudocompact type the weak glueing condition (when it applies) is necessary for smoothability. As an application we confirm the lifting property of specific divisors on the metric graph associated with a certain regular smoothing family, and give a new proof of a result of Cartright, Jensen, and Payne for vertex-avoiding divisors, and generalize it for divisors of rank one in the sense that, for the metric graph, there could be at most three edges (instead of two) between any pair of adjacent vertices.