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arXiv · 1212.0718

Containments of symbolic powers of ideals of generic points in $\PP^3$

Marcin Dumnicki
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Abstract

We show that the Conjecture of Harbourne and Huneke, $I^{(Nr-(N-1))} \subset M^{(r-1)(N-1)}I^{r}$ holds for ideals of generic (simple) points in $\PP^3$. As a result, for such ideals we prove the following bounds, which can be recognized as generalizations of Chudnovsky bounds: $α(I^{(3m-k)}) \geq mα(I)+2m-k$, for any $m \geq 1$ and $k=0,1,2$. Moreover, we obtain lower bounds for the Waldshmidt constant for such ideals.

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Marcin Dumnicki. 2012-12-04. Containments of symbolic powers of ideals of generic points in $\PP^3$. https://arxiv.org/abs/1212.0718

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