Representations of SL_2 and the distribution of points in P^n

Details Representations of SL_2 and the distribution of points in P^n Representations of SL_2 and the distribution of points in P^n

2002-11-15

arxiv.org/abs/math/0211245v1

Mathematics

Algebraic Geometry

Scientific paper

It is an open problem to determine the dimension of the space of homogeneous polynomials of a fixed degree vanishing at finitely many points in the projective plane to certain multiplicities. We present various aspects of this problem and a version of a known algorithm (originally due to M. Nagata) to compute this dimension for nine or less points. Our methods are completely elementary and only involve the representation theory of SL_2.

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