The blowing up Horace method: Application to interpolation in degree four
type: Item
instance of: scholarly article
title: The blowing up Horace method: Application to interpolation in degree four
zbMATH Open document ID: 0784.14002
DOI: 10.1007/BF01231903
published in: Inventiones Mathematicae
publication date: 1992-07-22T00:00:00Z
full work available at URL: https://eudml.org/doc/143979
review text: Here it is proved the following theorem which completes the case of polynomials of degree \(d \geq 5\) proved by \textit{J. Alexander} [Compos. Math. 68, No. 3, 305-354 (1988; Zbl 0675.14025)]. Theorem A: In the vector space of homogeneous polynomials of degree \(\leq 4\) in \(n\) variables over an infinite field the subspace formed by the polynomials vanishing together with their first derivatives at \(r\) sufficiently general points \(P_ 1,\ldots,P_ r\) has codimension \(r(n+1)\) (i.e. the expected one). -- The main point of the paper is the proof which shows how strong for these problems the many versions of Horace method are in the hands of the authors. Here the authors introduce and use a variant in which the inductive step is carried over a blowing up of the original variety \(X\) \((\mathbb{P}^ n\) for theorem A) on which one wants to prove a theorem on the cohomology groups of the general element of a family of subschemes of \(X\).
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 39402
zbMATH Keywords: homogeneous polynomials
zbMATH Keywords: Horace method
zbMATH Keywords: blowing up
author: James Alexander
author: André Hirschowitz
MaRDI profile type: Publication
cites work: Q3829660
cites work: La methode d'Horace pour l'interpolation à plusieurs variables
cites work: On the homogeneous ideal of the generic union of lines in 3.
OpenAlex ID: W2912135602
description: scientific article; zbMATH DE number 39402