Reduction theory of point clusters in projective space

Titelangaben

Stoll, Michael:
Reduction theory of point clusters in projective space.
In: Groups, Geometry, and Dynamics. Bd. 5 (2011) Heft 2 . - S. 553-565.
ISSN 1661-7207
DOI: https://doi.org/10.4171/GGD/139

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Abstract

We generalise earlier results of John Cremona and the author on the reduction theory of binary forms, whose zeros give point clusters in P^1, to point clusters in projective spaces P^n of arbitrary dimension. In particular, we show how to find a reduced representative in the SL(n+1,Z)-orbit of a given cluster. As an application, we show how one can find a unimodular transformation that produces a small equation for a given smooth plane curve.