%0 DATA
%A Elisa, Postinghel
%D 2017
%T A new proof of the Alexander-Hirschowitz interpolation theorem
%U https://repository.lboro.ac.uk/articles/A_new_proof_of_the_Alexander-Hirschowitz_interpolation_theorem/9388790
%2 https://repository.lboro.ac.uk/ndownloader/files/17002034
%K Degenerations
%K Polynomial interpolation
%K Linear systems
%K Double points
%X The 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.