Lyubeznik table of sequentially Cohen-Macaulay rings

TL;DR

This paper proves that certain classes of sequentially Cohen-Macaulay rings have trivial Lyubeznik tables, providing new insights into their algebraic structure and configurations based on deficiency modules.

Contribution

It establishes that sequentially Cohen-Macaulay rings in positive characteristic and Stanley-Reisner rings in any characteristic have trivial Lyubeznik tables, expanding understanding of their invariants.

Findings

Sequentially Cohen-Macaulay rings in positive characteristic have trivial Lyubeznik tables.

Stanley-Reisner rings in any characteristic also have trivial Lyubeznik tables.

Additional Lyubeznik table configurations are characterized by deficiency modules.

Abstract

We prove that sequentially Cohen-Macaulay rings in positive characteristic, as well as sequentially Cohen-Macaulay Stanley-Reisner rings in any characteristic, have trivial Lyubeznik table. Some other configurations of Lyubeznik tables are also provided depending on the deficiency modules of the ring.