In this paper, we study the fattening effect of points over the complex numbers for del Pezzo surfaces \(\mathbb {S}_r\) arising by blowing-up of \(\mathbb {P}^2\) at r general points, with \( r \in \{1, \dots , 8 \}\). Basic questions when studying the problem of points fattening on an arbitrary variety are what is the minimal growth of the initial sequence and how are the sets on which this minimal growth happens characterized geometrically. We provide a complete answer for del Pezzo surfaces.

中文翻译：

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点育肥对del Pezzo曲面的影响

在本文中，我们研究在对德尔Pezzo表面复数点的育肥效果\（\ mathbb {S} _r \）通过吹式所产生的\（\ mathbb {P} ^ 2 \）在ř一般分，带有\（r \ in \ {1，\ dots，8 \} \）。研究任意品种上的点育肥问题时的基本问题是，初始序列的最小增长是什么，以及最小增长发生在哪个集合上的几何特征如何。我们提供del Pezzo曲面的完整答案。