论文标题
沿分级分辨率的程度和贝蒂序列的边界
Bounds for the degree and Betti sequences along a graded resolution
论文作者
论文摘要
本文的主要目的是根据其生成程度来扩大均质理想的最小级别的自由分辨率。总的来说，这太雄心勃勃了。正如所理解的那样，大小的尺寸意味着仔细查看两个可用参数：移位和贝蒂数字。由于通常，偏移的界限可能会非常陡峭，因此我们通过Syzygies的子效率来滤除困难。我们采用的方法希望是新的，并为最小自由分辨率的结构提供了更多的启示。我们使用Boij-Söderberg技术来为Betti编号提供多项式上限。 预计超表面奇点的景观已经包含了任意案例的大多数困难角落。在这方面，我们对待此案的某些方面，包括改善了Busé-dimca-schenck-sticlaru最近作品的基本结果之一。
The main goal of this paper is to size up the minimal graded free resolution of a homogeneous ideal in terms of its generating degrees. By and large, this is too ambitious an objective. As understood, sizing up means looking closely at the two available parameters: the shifts and the Betti numbers. Since, in general, bounds for the shifts can behave quite steeply, we filter the difficulty by the subadditivity of the syzygies. The method we applied is hopefully new and sheds additional light on the structure of the minimal free resolution. We use the Boij-Söderberg techniques for the Betti numbers to get polynomial upper bounds for them. It is expected that the landscape of hypersurface singularities already contains most of the difficult corners of the arbitrary case. In this regard, we treat some facets of this case, including an improvement of one of the basic results of a recent work by Busé--Dimca--Schenck--Sticlaru.
