论文标题
关于广义乌尔里希模块的理论
On the theory of generalized Ulrich modules
论文作者
论文摘要
在本文中，我们进一步发展了Goto等人在2014年引入的广义Ulrich模块的理论。我们的主要目标是解决何时将HOM功能子和水平链接的操作保留乌尔里希属性的问题。应用之一是对二次超表面环的新表征。此外，在Gorenstein案例中，我们推断出将链接应用于Ulrich理想的足够高的Syzygy模块会产生Ulrich模块。最后，我们以最小的多重性来探索与模块理论的联系，作为副产品，我们确定了Ulrich模块的Chern数量以及其REES模块的Castelnuovo-Mummford规律性。
In this paper we further develop the theory of generalized Ulrich modules introduced in 2014 by Goto et al. Our main goal is to address the problem of when the operations of taking the Hom functor and horizontal linkage preserve the Ulrich property. One of the applications is a new characterization of quadratic hypersurface rings. Moreover, in the Gorenstein case, we deduce that applying linkage to sufficiently high syzygy modules of Ulrich ideals yields Ulrich modules. Finally, we explore connections to the theory of modules with minimal multiplicity, and as a byproduct we determine the Chern number of an Ulrich module as well as the Castelnuovo-Mumford regularity of its Rees module.
