论文标题
关于减少数字和Castelnuovo-Mumford的爆炸环和模块的规律性
On reduction numbers and Castelnuovo-Mumford regularity of blowup rings and modules
论文作者
论文摘要
我们证明了有关降低数量与爆炸代数和爆炸模块的Castelnuovo-Mumford规律性之间的连接的新结果，关键的基本工具是Ratliff-Rush关闭的操作。首先，我们在两种特殊情况下回答了M. E. Rossi，D。T. Trung和N. V. Trung关于二维Buchsbaum本地环中理想的Rees代数的问题，甚至我们甚至询问其中一种情况之一。在另一种定理中，我们通过将其扩展到任意维度（并允许相对于Cohen-Macaulay模块）将其扩展到二维Cohen-Macaulay局部环中的理想结果。我们得出许多应用，包括线性类型的（多项式）理想的表征，广义乌尔里希理想理论的进步以及其他作者的结果改进。
We prove new results on the connections between reduction numbers and the Castelnuovo-Mumford regularity of blowup algebras and blowup modules, the key basic tool being the operation of Ratliff-Rush closure. First, we answer in two particular cases a question of M. E. Rossi, D. T. Trung, and N. V. Trung about Rees algebras of ideals in two-dimensional Buchsbaum local rings, and we even ask whether one of such situations always holds. In another theorem we generalize a result of A. Mafi on ideals in two-dimensional Cohen-Macaulay local rings, by extending it to arbitrary dimension (and allowing for the setting relative to a Cohen-Macaulay module). We derive a number of applications, including a characterization of (polynomial) ideals of linear type, progress on the theory of generalized Ulrich ideals, and improvements of results by other authors.
