Freeness for complete intersections with an introduction to Cohen-Macaulay modules (1 and 2)

2017年   10月 19日 10時 30分 ~ 2017年   10月 26日 12時 00分
Delphine Pol (Hokkaido University)
DGS Seminar 002

(1) 2017/10/19 10:30-12:00 (Rm 3-413)
(2) 2017/10/26 10:30-12:00 (Rm 3-413)

The purpose of these two talks is to study a generalization to higher codimensional subspaces of the notion of Saito free divisors.
Before considering this subject, I will give a short introduction to Cohen-Macaulay modules, which is a notion used to define free singularities. I will first recall facts on regular sequences and depth in order to define Cohen-Macaulay modules and I will give some of their properties.
I will then recall the case of free divisors, then I will give the definition of multi-logarithmic forms along a reduced complete intersection which is suggested by Aleksandrov and Tsikh. I will then extend some of the characterizations of freeness for divisors to complete intersections. These notions and results can be generalized to reduced Cohen-Macaulay subspaces of a smooth variety. The results presented here are part of my PhD thesis.