The dominant rational maps of finite degree from a fixed variety to varieties of general type, up to birational isomorphisms, form a finite set. This has been known as the Iitaka-Severi conjecture, and is nowdays an established result, in virtue of some recent advances in the theory of pluricanonical maps. We study the question of finding some effective estimate for the finite number of maps, and to this aim we provide some update and refinement of the classical treatment of the subject.

中文翻译：

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关于各种一般类型的有理图的有限性定理

从固定品种到一般类型的品种，直至双边同构的有限度的主导有理图形成一个有限集。这被称为Iitaka-Severi猜想，并且由于在古皮图谱理论上的一些最新进展，如今已成为一个确定的结果。我们研究了为有限数量的图寻找有效估计的问题，为此，我们对主题的经典处理方法进行了一些更新和完善。