La methode d'Horace pour l'interpolation à plusieurs variables
type: Item
instance of: scholarly article
title: La methode d'Horace pour l'interpolation à plusieurs variables
zbMATH Open document ID: 0571.14002
DOI: 10.1007/BF01168836
published in: Manuscripta Mathematica
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155059
review text: Here the author considers several maximal rank type problems for zero- dimensional subschemes of \({\mathbb{P}}^ n\). He rises several conjectures and develops a general method to attack them. He applies his method in particular cases. For instance he shows for \(k=2\), \(t=2\) or 3 and for \(k=3\), \(t=2\), at how many general points it is possible to prescribe values and derivatives up to order t-1 to a polynomial of given degree in k variables. The proofs use modern projective geometry (Hilbert schemes, semicontinuity) and a very refined inductive procedure.
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 12D10
zbMATH DE Number: 3910523
zbMATH Keywords: Hilbert scheme
zbMATH Keywords: postulation
zbMATH Keywords: Newton polygon
zbMATH Keywords: interpolation
zbMATH Keywords: maximal rank
zbMATH Keywords: zero-dimensional subschemes
author: André Hirschowitz
MaRDI profile type: Publication
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OpenAlex ID: W2913429953
description: scientific article; zbMATH DE number 3910523