三点亏缺正则曲面

Luca Chiantini; Thomas Markwig

三点亏缺正则曲面

代数几何 2009-11-06 v2

作者: Luca Chiantini , Thomas Markwig

摘要

本文研究了通过非常丰沛线丛 $L$ 嵌入的曲面 $S$ 的超平面截面线性系 $|L-3p|$ ，其中 $p$ 为一般点且具有三重奇点。如果该线性系不具备期望维数，我们称 $(S,L)$ 为三点亏缺（triple-point defective）。我们证明了在三点亏缺正则曲面上，过一般点的每个超平面截面要么具有一个三重分支，要么该曲面是有理直纹面且该超平面截面包含直纹纤维的两倍。

关键词

incidence geometry of points and lines algebraic surfaces surfaces and embeddings

引用

@article{arxiv.0705.3912,
  title  = {Triple-Point Defective Regular Surfaces},
  author = {Luca Chiantini and Thomas Markwig},
  journal= {arXiv preprint arXiv:0705.3912},
  year   = {2009}
}

The results of this paper have been generalised in the paper Triple point defective surfaces (arXiv:0911.1222) by the same authors. The assumptions on the linear system and on the surface have been weakened. Large parts of the new paper coincide with this old paper and the reader should rather refer to the new paper than to this old one

三点亏缺正则曲面

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