A new proof of the Alexander-Hirschowitz interpolation Theorem

2010/03/01 by Elisa Postinghel, Postinghel, Elisa · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #math.AG #msc:14C20 #msc:14D06 #msc:14N05

paper · pdf · doi:10.48550/arxiv.1003.0323

15 pages

Abstract

The classical polynomial interpolation problem in several variables can be generalized to the case of points with greater multiplicities. What is known, as yet, 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.

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• Secant varieties of Segre-Veronese embeddings of (P¹)^r

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