报告时间：2022/10/18 13:30-14:30

腾讯会议：490-560-155

报告题目：Noncommutative Segre products

摘要：In noncommutative algebraic geometry, the analogue of projective space $\mathbb{P}^{n-1}$ is the quotient category $qgr-A := gr-A/tors-A$, where $A$ is a Noetherian $\mathb{ N}$-graded Artin-Schelter regular global dimension $n$, and $gr-A$ is the category of finitely generated graded right $A$-modules, $tors-A$ is the full subcategory of finite dimensional modules. In order to understand a noncommutative version of the classical Segre embedding of $\mathbb{P}^{n-1}\times \mathbb{P}^{m-1}\to \mathbb{P}^{nm-1}$, we introduced the notion of twisted Segre products of Noetherian $\mathbb{N}$-graded algebras. It is proved that the twisted Segre product of two Koszul Noetherian Artin-Schelter regular algebras is a graded isolated singularity. In the simplest case, the Cohen-Macaulay representations of twisted Segre products of $k[x,y]$ with itself are computed.

报告人简介：何济位，杭州师范大学数学学院教授、副院长，2004年毕业于浙江大学数学系，获博士学位。2004年9月至2012年02月先后在复旦大学数学学院和比利时安特卫普大学从事博士后研究工作。浙江省“151人才（第三层次）”，省高校中青年学科带头人。主持国家自然科学基金面上项目2项，青年基金1项，省部级基金4项。主要研究领域为非交换代数，在Trans AMS、J Noncommut Geom、Math Z、Israel J Math、J Algebra、中国科学等国内外重要期刊上发表学术论文30余篇。