射影空间中点簇的约化理论
Reduction theory of point clusters in projective space
摘要：
在本文中，我们把约翰·克雷莫纳和作者早先关于描述P^1中正零圈的二元形式的约化理论的结果推广到任意维射影空间中的正零圈（或点簇）。这应该可以应用于P^n中更一般的投射簇，通过以PGL（n+1）-不变的方式将一个合适的正零圈与它们联系起来。我们在（光滑）平面曲线的情况下讨论这一点。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
