高维基本极小值和循环的均匀分布

Pub Date : 2020-01-30 DOI:10.5802/aif.3500
R. Gualdi, C. Mart'inez
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引用次数: 0

摘要

本质极小值和小点的等分布是算术几何中两个公认的相互关联的主题。然而,缺乏处理高维子变体的本质极小值的类似物,并且这些子变体的均匀分布是一个远未被探索的主题。在本文中,我们引入了一个新的高维本质极小的概念,并用它来证明一般有效环和小有效环的等分布。后者通过考虑循环和在算术数据上允许更多的灵活性来推广先前的高维等分布定理。
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Higher dimensional essential minima and equidistribution of cycles
The essential minimum and equidistribution of small points are two well-established interrelated subjects in arithmetic geometry. However, there is lack of an analogue of essential minimum dealing with higher dimensional subvarieties, and the equidistribution of these is a far less explored topic. In this paper, we introduce a new notion of higher dimensional essential minimum and use it to prove equidistribution of generic and small effective cycles. The latter generalizes the previous higher dimensional equidistribution theorems by considering cycles and by allowing more fexibility on the arithmetic datum.
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