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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Containments of symbolic powers of ideals of generic points in $\mathbb {P}^3$
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by Marcin Dumnicki PDF
Proc. Amer. Math. Soc. 143 (2015), 513-530 Request permission

Abstract:

We show that the Conjecture of Harbourne and Huneke, stating that $I^{(Nr-(N-1))} \subset M^{(r-1)(N-1)}I^{r}$ for ideals of points in $\mathbb {P}^N$, holds for generic (simple) points for $N = 3$. As a result, for such ideals we prove the following bounds, which can be recognized as generalizations of Chudnovsky bounds: $\alpha (I^{(3m-k)}) \geq m\alpha (I)+2m-k$, for any $m \geq 1$ and $k=0,1,2$. Moreover, we obtain lower bounds for the Waldschmidt constant for such ideals.
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Additional Information
  • Marcin Dumnicki
  • Affiliation: Institute of Mathematics, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland
  • MR Author ID: 692599
  • Email: Marcin.Dumnicki@im.uj.edu.pl
  • Received by editor(s): November 29, 2012
  • Received by editor(s) in revised form: May 17, 2013
  • Published electronically: October 31, 2014
  • Communicated by: Lev Borisov
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 513-530
  • MSC (2010): Primary 14Q10, 13P10
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12273-8
  • MathSciNet review: 3283641