On the Alexander-Hirschowitz Theorem
| dc.creator | Brambilla, Maria Chiara | |
| dc.creator | Ottaviani, Giorgio | |
| dc.date | 2007-01-15 | |
| dc.date | 2007-09-10 | |
| dc.date.accessioned | 2026-07-07T08:28:17Z | |
| dc.date.available | 2026-07-07T08:28:17Z | |
| dc.description | The Alexander-Hirschowitz theorem says that a general collection of $k$ double points in ${\bf P}^n$ 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. | |
| dc.description | 29 pages, the proof in the case of cubics has been simplified, three references added, to appear in J. Pure Appl. Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0701409 | |
| dc.identifier | http://arxiv.org/abs/math/0701409 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137562 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | History and Overview | |
| dc.subject | 01-02; 14C20; 15A72; 14M17 | |
| dc.title | On the Alexander-Hirschowitz Theorem | |
| dc.type | text |