JournalsggdVol. 5, No. 2pp. 553–565

Reduction theory of point clusters in projective space

  • Michael Stoll

    Universität Bayreuth, Germany
Reduction theory of point clusters in projective space cover
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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 P1\mathbb{P}^1, to point clusters in projective spaces Pn\mathbb{P}^n of arbitrary dimension. In particular, we show how to find a reduced representative in the SL(n+1,Zn+1, \mathbb{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.

Cite this article

Michael Stoll, Reduction theory of point clusters in projective space. Groups Geom. Dyn. 5 (2011), no. 2, pp. 553–565

DOI 10.4171/GGD/139