Campana points of bounded height on vector group compactifications
Campana points of bounded height on vector group compactifications
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DOI：
10.1112/plms.12391
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发表时间：
2019-08
影响因子：
1.8
通讯作者：
Marta Pieropan;A. Smeets;Sho Tanimoto;Anthony Várilly-Alvarado
中科院分区：
文献类型：
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作者：
Marta Pieropan;A. Smeets;Sho Tanimoto;Anthony Várilly-Alvarado
本文对法诺轨道上的加权边界除数积分的有理点子集进行了系统的定量研究。我们称这些集合中的点为坎帕纳点。坎帕纳和随后的阿布拉莫维奇的早期工作表明，坎帕纳点有几个合理的相互竞争的定义。我们使用了一个版本，它可以很好地描述不同类型的点的行为，因为边界除数上的权重不同。这提出了一个关于满足klt （Kawamata log terminal）条件的Campana点集的Fano轨道的Manin型猜想。通过引入Chambert‐Loir和Tschinkel的工作，我们证明了关于向量群的等变紧化的klt Campana点的Manin猜想的一个对数版本。
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.