English

Reduction theory of point clusters in projective space

Number Theory 2016-08-03 v1 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.0909.2808,
  title  = {Reduction theory of point clusters in projective space},
  author = {Michael Stoll},
  journal= {arXiv preprint arXiv:0909.2808},
  year   = {2016}
}

Comments

12 pages

R2 v1 2026-06-21T13:46:41.412Z