On the Alexander-Hirschowitz Theorem

Details On the Alexander-Hirschowitz Theorem On the Alexander-Hirschowitz Theorem

2007-01-15

arxiv.org/abs/math/0701409v2

Mathematics

Algebraic Geometry

29 pages, the proof in the case of cubics has been simplified, three references added, to appear in J. Pure Appl. Algebra

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On the Alexander-Hirschowitz Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Alexander-Hirschowitz Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Alexander-Hirschowitz Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-585370