Abstract Our aim in this work is to study exact Osserman limit linear series on curves of compact type X with three irreducible components. This case is quite different from the case of two irreducible components studied by Osserman. For instance, for curves of compact type with two irreducible components, every refined Eisenbud-Harris limit linear series has a unique exact extension. But, for the case of three irreducible components, this property is no longer true. We find a condition characterizing when a given refined Eisenbud-Harris limit linear series has a unique exact extension. To do this, it is necessary to understand how to construct exact extensions. We find a constructive method, which describes how to construct all exact extensions of refined limit linear series. By our method, we get that every refined limit linear series has at least one exact extension.

中文翻译：

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具有三个不可约分量的紧凑型曲线的极限线性级数

摘要 我们在这项工作中的目的是研究具有三个不可约分量的紧凑型 X 曲线上的精确 Osserman 极限线性级数。这种情况与 Osserman 研究的两个不可约分量的情况大不相同。例如，对于具有两个不可约分量的紧凑型曲线，每个细化的 Eisenbud-Harris 极限线性级数都有唯一的精确扩展。但是，对于三个不可约分量的情况，这个性质不再成立。我们发现了一个条件，它表征给定的 Eisenbud-Harris 极限线性系列具有独特的精确扩展。为此，有必要了解如何构造精确的扩展。我们找到了一种构造方法，它描述了如何构造精化极限线性级数的所有精确扩展。按照我们的方法，