PG（2，q）中二次曲线内点的线划分
Line partitions of internal points to a conic in PG(2,q)
摘要：
确定PG（2，q）中的圆锥曲线C的内部点集的所有分割线集，q为奇数。只有三个这样的线集，即通过C的外部点到C的所有非切线的集合，通过C中的点到C的所有非切线的集合，以及对于平方q，属于至少有5个公共点的Baer子平面的所有非切线的集合。这一分类定理类似于塞格雷和卡马罗斯的经典结果，他们把通过一个内部点到C的线束描述为唯一的直线集，直到射影，它提供了到C的所有非内部点的集合的一个划分。然而，证明是不类似的，因为它不依赖于著名的引理的塞格雷切线。本文的主要工具是C的所有内部点的集合在二次曲线上的某些划分，以及非割线的阻塞集和外部线的阻塞集的一些最近的组合特征。
英文摘要：
All sets of lines providing a partition of the set of internal points to a conic C in PG(2,q), q odd, are determined. There exist only three such linesets up to projectivities, namely the set of all nontangent lines to C through an external point to C, the set of all nontangent lines to C through a point in C, and, for square q, the set of all nontangent lines to C belonging to a Baer subplane with at least 5 common points with C. This classification theorem is the analogous of a classical result by Segre and Korchmaros characterizing the pencil of lines through an internal point to C as the unique set of lines, up to projectivities, which provides a partition of the set of all noninternal points to C. However, the proof is not analogous, since it does not rely on the famous Lemma of Tangents of Segre. The main tools in the present paper are certain partitions in conics of the set of all internal points to C, together with some recent combinatorial characterizations of blocking sets of non-secant lines, and of blocking sets of external lines.
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