Zero Cells of the Siegel-Gottschling Fundamental Domain of Degree 2
Zero Cells of the Siegel-Gottschling Fundamental Domain of Degree 2
复制标题
2 阶 Siegel-Gottschling 基本域的零单元
DOI：
10.1080/10586458.2012.653273
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Takahiro Hayata
中科院分区：
文献类型：
--
作者：
Kikkawa;Takeo;Takahiro Hayata
设是关于Siegel模群的Siegel上半度空间的基本整环。根据西格尔自己的说法，它只由100多个多项式不等式决定。在degreen=2的情况下，Gottschling确定了不等式的最小集合。的边界是非常关注的文献不仅从同调的角度来看，而且从几何的数字。在本文中，我们计算的条件下，定义的理想是零维（“0-细胞”）的顶点。我们还讨论了0-细胞之间的等价关系。
Let be a fundamental domain of the Siegel upper half-space of degreenwith respect to the Siegel modular group . According to Siegel himself, is determined by only finitely many polynomial inequalities. In case of degreen=2, Gottschling determined the minimal set of inequalities. The boundary of is of great concern in the literature not only from a homological point of view but also from the geometry of numbers. In this paper we compute the vertices of under the condition that the defining ideal is zero-dimensional (“0-cells”). We also discuss an equivalence relation among 0-cells.