Geometric Aspects of Polynomial Interpolation in More Variables and of Waring's Problem [chapter]

Ciro Ciliberto
2001 European Congress of Mathematics  
In this paper I treat the problem of determining the dimension of the vector space of homogeneous polynomials in a given number of variables vanishing with some of their derivatives at a finite set of general points in projective space. I will illustrate the geometric meaning of this problem and the main results and conjectures about it. I will finally point out its connection with the so-called Waring's problem for forms, of which I will also indicate the geometric meaning.
doi:10.1007/978-3-0348-8268-2_17 fatcat:vhuwih3exrcvjjfki32u3zarqm