射影空间中重点Hilbert函数的组合界
代数几何
2010-12-14 v3 交换代数
摘要
我们研究了射影空间中由有限点集支撑的某些非还原概形A的Hilbert函数，特别是重点概形。我们仅利用点的重数以及关于点的哪些子集线性相关的信息，给出了A的Hilbert函数的组合定义的上下界。当N=2时，我们显式地给出了这些界，并给出了上下界相等的充分判据。当该判据满足时，我们给出了A的Hilbert函数的简单公式，以及定义A的理想的分次Betti数的组合定义的上下界，推广了Geramita-Migliore-Sabourin（2006）的结果。对于许多在组合学、几何学和代数上具有趣味的例子族，我们获得了精确的Hilbert函数和分次Betti数。我们的方法适用于任何特征。实现我们结果的AWK脚本可从http://www.math.unl.edu/~bharbourne1/CHT/Example.html获取。
引用
@article{arxiv.0912.1915,
title = {Combinatorial bounds on Hilbert functions of fat points in projective space},
author = {Susan Cooper and Brian Harbourne and Zach Teitler},
journal= {arXiv preprint arXiv:0912.1915},
year = {2010}
}
备注
23 pages; changes have been made following suggestions of the referee; explicit statements are now included for dimensions greater than 2, hence the title no longer mentions the plane; however the content is largely the same as in the previous version; this version is to appear in the Journal of Pure and Applied Algebra