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Koszul Complexes and Pole Order Filtrations

组织者

丘成栋

演讲者

胡创强

时间

2022年10月07日 14:00 至 15:00

地点

Online

摘要

In this talk, we will review the work: Koszul Complexes and Pole Order Filtrations, by Alexandru Dimca and Gabriel Sticlaru. We study the interplay between the cohomology of the Koszul complex of the partial derivatives of a homogeneous polynomial f and the pole order filtration $P$ on the cohomology of the open set $U = P^n setminus D$, with $D$ the hypersurface defined by $f = 0$. The relation is expressed by some spectral sequences, which may be used on one hand to determine the filtration $P$ in many cases for curves and surfaces, and on the other hand to obtain information about the syzygies involving the partial derivatives of the polynomial $f$.

演讲者介绍

胡创强，2021年秋季入职BIMSA。主要研究领域包括：编码理论，函数域及数论，奇点理论。近年来在量子码，代数几何码，Drinfeld模，椭圆奇点，丘-李代数等课题研究中取得了一系列学术成就。在《IEEE Trans. on IT.》《Finite Fields and Their Applications》《Designs, Codes and Cryptography》等著名学术期刊上发表论文13篇。先后多次应邀出席国内外学术会议并作大会报告。