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A new proof of the Alexander-Hirschowitz interpolation theorem
journal contribution
posted on 2017-06-02, 12:57 authored by Elisa PostinghelThe classical polynomial interpolation problem in several variables can be generalized to the case of points with greater multiplicities. What is known so far is essentially concentrated in the Alexander-Hirschowitz Theorem which says that a general collection of double points in P r gives independent conditions on the linear system L of the hypersurfaces of degree d, with a well known list of exceptions. We present a new proof of this theorem which consists in performing degenerations of P r and analyzing how L degenerates. © 2010 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.
History
School
- Science
Department
- Mathematical Sciences
Published in
Annali di Matematica Pura ed ApplicataVolume
191Issue
1Pages
77 - 94Citation
POSTINGHEL, E., 2012. A new proof of the Alexander-Hirschowitz interpolation theorem. Annali di Matematica Pura ed Applicata, 191(1), pp. 77-94.Publisher
© SpringerVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2012Notes
The final publication is available at Springer via http://dx.doi.org/10.1007/s10231-010-0175-9ISSN
0373-3114eISSN
1618-1891Publisher version
Language
- en