On the Alexander-Hirschowitz Theorem
نویسندگان
چکیده
The Alexander-Hirschowitz theorem says that a general collection of k double points in P 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. AMS Subject Classification: 01-02, 14C20, 15A72, 14M17 Both authors are partially supported by Italian MUR and are members of GNSAGA.
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