理想序列的赋值与渐近不变量
代数几何
2011-10-21 v3 交换代数
摘要
我们研究了分次理想序列的渐近跳跃数，并证明了每个这样的不变量都由函数域上的某个实赋值计算得出。我们猜想每个计算渐近跳跃数的赋值必然是拟单项式的。该猜想在二维情形下成立。一般情况下，我们将其归结为仿射空间和赋值理想的分次序列的情形。在此过程中，我们研究了某个适当赋值空间的结构。
引用
@article{arxiv.1011.3699,
title = {Valuations and asymptotic invariants for sequences of ideals},
author = {Mattias Jonsson and Mircea Mustata},
journal= {arXiv preprint arXiv:1011.3699},
year = {2011}
}
备注
49 pages; v2: we now work more generally in the setting of arbitrary excellent regular schemes; some details regarding the definition of quasi-monomial valuations have been added in Section 3.1; v3: minor changes, this is the final version, to appear in Ann. Inst. Fourier (Grenoble)