论文标题
对多面式理想的根本支持
Radical support for multigraded ideals
论文作者
论文摘要
可以通过查看发电机的程度来判断理想是否是激进的？总的来说，这是绝望的。但是，在多层的多项式环中有特殊的学位，其特性是由这些学位元素产生的任何多层理想是根本的。我们称这样的学位为根本支持。在本文中，我们给出了自由基支持的组合表征。我们的表征是在相关标记的图中在循环的特性方面。我们还表明，激进支持的概念与Cartwright-Sturmfels理想密切相关。实际上，任何由多层的发电机产生的理想形成了多面形，构成根本支撑的理想是Cartwright-Sturmfels的理想。相反，一系列学位的集合使得Cartwright-Sturmfels都是由这些程度的元素产生的任何多面式理想都是一种根本的支持。
Can one tell if an ideal is radical just by looking at the degrees of the generators? In general, this is hopeless. However, there are special collections of degrees in multigraded polynomial rings, with the property that any multigraded ideal generated by elements of those degrees is radical. We call such a collection of degrees a radical support. In this paper, we give a combinatorial characterization of radical supports. Our characterization is in terms of properties of cycles in an associated labelled graph. We also show that the notion of radical support is closely related to that of Cartwright-Sturmfels ideals. In fact, any ideal generated by multigraded generators whose multidegrees form a radical support is a Cartwright-Sturmfels ideal. Conversely, a collection of degrees such that any multigraded ideal generated by elements of those degrees is Cartwright-Sturmfels is a radical support.
