Geodesic
Reduction theory of point clusters in projective space
Michael Stoll1
1Universität Bayreuth, Germany
Groups, geometry, and dynamics, Tome 5 (2011) no. 2, pp. 553-565

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DOI

We generalise earlier results of John Cremona and the author on the reduction theory of binary forms, whose zeros give point clusters in P1, to point clusters in projective spaces Pn 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.
DOI : 10.4171/ggd/139
Classification : 11-XX, 00-XX
Mots-clés : Reduction theory, point clusters

Michael Stoll  1

1 Universität Bayreuth, Germany 
Michael Stoll. Reduction theory of point clusters in projective space. Groups, geometry, and dynamics, Tome 5 (2011) no. 2, pp. 553-565. doi: 10.4171/ggd/139
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     number = {2},
     doi = {10.4171/ggd/139},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/139/}
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