On the containment problem for fat points ideals and Harbourne’s conjecture

Tohǎneanu, Ştefan; Xie, Yu

doi:10.1090/proc/14943

On the containment problem for fat points ideals and Harbourne’s conjecture
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by Ştefan O. Tohǎneanu and Yu Xie PDF

Proc. Amer. Math. Soc. 148 (2020), 2411-2419 Request permission

Abstract:

In this note we show that Harbourne’s conjecture is true for symbolic powers of fat points ideals, and we check that the stable version of this conjecture is valid for ideals of very general points (resp., generic points) in $\mathbb P_{\mathbb K}^N$ (resp., $\mathbb P_{\mathbb K(\underline {z})}^N$), where $\mathbb {K}$ is a field of characteristic 0. We also show that this conjecture and the Harbourne-Huneke conjecture are true for a class of ideals $I$ defining fat points obtained from line arrangements in $\mathbb P_{\mathbb K}^2$.

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