A containment result in $P^n$ and the Chudnovsky Conjecture
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- by Marcin Dumnicki and Halszka Tutaj-Gasińska
- Proc. Amer. Math. Soc. 145 (2017), 3689-3694
- 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 $\mathbb {P}^n$.References
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Bibliographic Information
- Marcin Dumnicki
- Affiliation: Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland
- MR Author ID: 692599
- 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
- MR Author ID: 612578
- Email: Halszka.Tutaj-Gasinska@uj.edu.pl
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3689-3694
- MSC (2010): Primary 13A15, 13A02
- DOI: https://doi.org/10.1090/proc/13582
- MathSciNet review: 3665024