The depth descending problem of symbolic powers and local cohomology with respect to edge ideals of very well-covered graphs

Thời gian: 14:00 đến 16:00 Ngày 05/09/2024

Địa điểm: C101, VIASM

Báo cáo viên: Naoki Terai (Okayama University)

Abstract: First I talk about some partial results on the depth descending problem on symbolic powers of edge ideals of simple graphs, including the case of very well-covered graphs. This part is based on a joint work with K.Kimura and S. Yassemi.
Next I talk about the structure of (non-Cohen-Macaulay) very well-covered graphs, and the Hilbert function of the local cohomology modules of the residue ring by the edge ideal of a very well-covered graph. I give formulas on its depth and regularity using it. This part is based on a joint work with M.R.Pournaki, M. Poursolani and S.Yassemi.
If time permits, I talk about similar results on multi-whisker graphs, which is a joint work with Y. Muta.