%0 Journal Article
%T Reduction theory of point clusters in projective space
%A Michael Stoll
%J Mathematics
%D 2009
%I arXiv
%X In this paper, we generalise results obtained earlier by John Cremona and the author on the reduction theory of binary forms, which describe positive zero-cycles in P^1, to positive zero-cycles (or point clusters) in projective spaces of arbitrary dimension. This should have applications to more general projective varieties in P^n, by associating a suitable positive zero-cycle to them in an PGL(n+1)-invariant way. We discuss this in the case of (smooth) plane curves.
%U http://arxiv.org/abs/0909.2808v1