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Seminar on Algebraic, Complex Geometry and Singularities
Koszul Complexes and Pole Order Filtrations
Koszul Complexes and Pole Order Filtrations
Organizer
Speaker
Time
Friday, October 7, 2022 2:00 PM - 3:00 PM
Venue
Online
Abstract
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 $f$.
Speaker Intro
Hu chuangqiang joined Bimsa in the autumn of 2021. The main research fields include: coding theory, function field and number theory, singularity theory. In recent years, he has made a series of academic achievements in the research of quantum codes, algebraic geometric codes, Drinfeld modules, elliptic singular points, Yau Lie algebras and other studies. He has published 13 papers in famous academic journals such as IEEE Trans. on IT., Final Fields and their Applications, Designs, Codes and Cryptography. He has been invited to attend domestic and international academic conferences for many times and made conference reports.