We initiate a systematic quantitative study of subsets of rational points that are integral with respect to a weighted boundary divisor on Fano orbifolds. We call the points in these sets Campana points. Earlier work of Campana and subsequently Abramovich shows that there are several reasonable competing definitions for Campana points. We use a version that delineates well different types of behavior of points as the weights on the boundary divisor vary. This prompts a Manin-type conjecture on Fano orbifolds for sets of Campana points that satisfy a klt (Kawamata log terminal) condition. By importing work of Chambert-Loir and Tschinkel to our setup, we prove a log version of Manin's conjecture for klt Campana points on equivariant compactifications of vector groups.

中文翻译：

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向量群紧致上有界高度的坎帕纳点

我们开始对 Fano orbifolds 上的加权边界除数积分的有理点子集进行系统的定量研究。我们称这些集合中的点为 Campana 点。Campana 和随后的 Abramovich 的早期工作表明，Campana 点有几个合理的相互竞争的定义。当边界除数的权重不同时，我们使用一个版本来描述点的不同类型的行为。对于满足 klt（Kawamata 对数终端）条件的 Campana 点集，这提示了对 Fano orbifolds 的 Manin 类型猜想。通过将 Chambert-Loir 和 Tschinkel 的工作导入我们的设置，我们证明了 Manin 猜想的对数版本，用于 klt Campana 点对向量群的等变紧化。