The Alexander-Hirschowitz theorem says that a general collection of k double points in Pn imposes independent conditions on homogeneous polynomials of degree d with a well known list of exceptions. Alexander and Hirschowitz completed its proof in 1995, solving a long standing classical problem, connected with the Waring problem for polynomials. We expose a self-contained proof based mainly on previous works by Terracini, Hirschowitz, Alexander and Chandler, with a few simplifications. We claim originality only in the case d = 3, where our proof is shorter. We end with an account of the history of the work on this problem.

On the Alexander-Hirschowitz theorem / Brambilla, Maria Chiara; G., Ottaviani. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 212 (5):(2008), pp. 1229-1251.

On the Alexander-Hirschowitz theorem.

BRAMBILLA, Maria Chiara;
2008-01-01

Abstract

The Alexander-Hirschowitz theorem says that a general collection of k double points in Pn imposes independent conditions on homogeneous polynomials of degree d with a well known list of exceptions. Alexander and Hirschowitz completed its proof in 1995, solving a long standing classical problem, connected with the Waring problem for polynomials. We expose a self-contained proof based mainly on previous works by Terracini, Hirschowitz, Alexander and Chandler, with a few simplifications. We claim originality only in the case d = 3, where our proof is shorter. We end with an account of the history of the work on this problem.
2008
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/38817
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