标题： 有限射影平面上的阻塞半有效集的推广 显示英文标题

标题： Generalizing blocking semiovals in finite projective planes

摘要： 阻塞半椭圆以及确定其(最小)大小是有限射影几何中的一个核心研究课题。 在本文中，我们引入了有限射影平面$\text{PG}(2,q)$中具有$r_\infty$属性的阻塞集的概念，其中$r_\infty$是一条线，$\text{PG}(2,q)$是$q$的素数幂。 这一概念极大地推广了阻塞半椭圆的概念。 我们研究确定那些整数$k$的问题，使得存在一个大小为$k$且具有$r_\infty$-性质的阻塞集。 为了解决这个问题，我们建立新的理论，深入分析有限射影和平面中的阻塞集之间的相互作用。 显示英文摘要

摘要： Blocking semiovals and the determination of their (minimum) sizes constitute one of the central research topics in finite projective geometry. In this article we introduce the concept of blocking set with the $r_\infty$-property in a finite projective plane $\text{PG}(2,q)$, with $r_\infty$ a line of $\text{PG}(2,q)$ and $q$ a prime power. This notion greatly generalizes that of blocking semioval. We address the question of determining those integers $k$ for which there exists a blocking set of size $k$ with the $r_\infty$-property. To solve this problem, we build new theory which deeply analyzes the interplay between blocking sets in finite projective and affine planes.