Abstract
In this paper, we generalise the results of [5] on the reduction theory of binary forms, which describe positive zero-cycles in P, to positive zero-cycles (or point clusters) in projective spaces of arbitrary dimension. This should have applications to more general projective varieties in P, by associating a suitable positive zerocycle to them in an PGL(n + 1)-invariant way. We discuss this in the case of (smooth) plane curves.
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