论文标题
静态态度，规范模块和剪切多型的规律性
Seminormality, canonical modules, and regularity of cut polytopes
论文作者
论文摘要
由stulmfels和sullivant的猜想激发，我们研究了正常的切割多面体。经过对正常切割多型的已知结果的简短调查，特别是观察到，对于简单和简单的剪切多型，它们的切割代数是正常的，因此cohen--macaulay。此外，还考虑了拟态性。结果表明，$ k_5 $的剪切代数不是半正常的，这再次暗示已知的事实是不正常的事实。对于正常的戈伦斯坦（Gorenstein）切断代数和其他感兴趣的案例，我们确定其规范模块。如果假定正态性，则根据各种类型的图形和边界计算Castelnuovo-Mumford的定期。作为应用程序，我们将剪切代数的规律性小于或等于4的所有图表进行分类。
Motivated by a conjecture of Sturmfels and Sullivant we study normal cut polytopes. After a brief survey of known results for normal cut polytopes it is in particular observed that for simplicial and simple cut polytopes their cut algebras are normal and hence Cohen--Macaulay. Moreover, seminormality is considered. It is shown that the cut algebra of $K_5$ is not seminormal which implies again the known fact that it is not normal. For normal Gorenstein cut algebras and other cases of interest we determine their canonical modules. The Castelnuovo-Mumford regularity of a cut algebra is computed for various types of graphs and bounds for it are provided if normality is assumed. As an application we classify all graphs for which the cut algebra has regularity less than or equal to 4.
