数域上的五次del Pezzo曲面上有界高度的点

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-10-06 DOI:10.1016/j.aim.2025.110561

Christian Bernert , Ulrich Derenthal

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引用次数: 0

摘要

我们证明了任意数域上分裂光滑五次del Pezzo曲面关于相当一般的反正则高度函数的Manin猜想。在传递到泛量之后，我们首先证明了我们可以将量变量限制到它们的典型尺寸，然后我们可以解决0最小结构框架下的计数问题。

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Points of bounded height on quintic del Pezzo surfaces over number fields

We prove Manin's conjecture for split smooth quintic del Pezzo surfaces over arbitrary number fields with respect to fairly general anticanonical height functions. After passing to universal torsors, we first show that we may restrict the torsor variables to their typical sizes, and then we can solve the counting problem in the framework of o-minimal structures.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.