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A containment result in $ P^n$ and the Chudnovsky Conjecture


Authors: Marcin Dumnicki and Halszka Tutaj-Gasińska
Journal: Proc. Amer. Math. Soc. 145 (2017), 3689-3694
MSC (2010): Primary 13A15, 13A02
DOI: https://doi.org/10.1090/proc/13582
Published electronically: February 22, 2017
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Abstract: In this paper we prove the containment $ I^{(nm)}\subset M^{(n-1)m}I^m$, for a radical ideal $ I$ of $ s$ general points in $ \mathbb{P}^n$, where $ s\geq 2^n$. As a corollary we get that the Chudnovsky Conjecture holds for a very general set of at least $ 2^n$ points in $ \mathbb{P}^n$.


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Marcin Dumnicki
Affiliation: Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland
Email: Marcin.Dumnicki@im.uj.edu.pl

Halszka Tutaj-Gasińska
Affiliation: Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland
Email: Halszka.Tutaj-Gasinska@uj.edu.pl

DOI: https://doi.org/10.1090/proc/13582
Keywords: Symbolic powers, fat points
Received by editor(s): March 13, 2016
Received by editor(s) in revised form: April 27, 2016, and September 27, 2016
Published electronically: February 22, 2017
Communicated by: Lev Borisov
Article copyright: © Copyright 2017 American Mathematical Society

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