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arXiv · 1308.4983

The effect of points fattening in dimension three

Thomas Bauer·Tomasz Szemberg
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Abstract

There has been increased recent interest in understanding the relationship between the symbolic powers of an ideal and the geometric properties of the corresponding variety. While a number of results are available for the two-dimensional case, the higher-dimensional case is largely unexplored. In the present paper we study a natural conjecture arising from a result by Bocci and Chiantini. As a first step towards understanding the higher-dimensional picture, we show that this conjecture is true in dimension three. Also, we provide examples showing that the hypotheses of the conjecture may not be weakened.

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Thomas Bauer, Tomasz Szemberg. 2013-08-22. The effect of points fattening in dimension three. https://arxiv.org/abs/1308.4983

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