Lyubeznik numbers of almost complete intersection and linked ideals

Abstract

In this work, we examine the Lyubeznik numbers of squarefree monomial ideals that are linked. Also we study these numbers for almost complete intersection ideals.

Certain endomorphism rings of local cohomology modules and Lyubeznik numbers

“…Recently, there has been interest in finding the form of Lyubeznik tables. For instance, the shape of Lyubeznik tables for sequentially, canonically Cohen-Macaulay [AM15], generalised Cohen-Macaulay and Buchsbaum modules [NRE20] are known; it is also known the case of almost complete intersection ideals under some additional conditions, see [NR22] for details. To do in this direction, in Section 4 we continue our consideration of Lyubeznik numbers of certain partially sequentially Cohen-Macaulay rings introduced in [SS17]; our main result (Theorem 4.10) shows the shape of the Lyubeznik table of an i-sequentially Cohen-Macaulay ring, which recovers and extends the fact, proved in [AM15, Proposition 4.1], that, under certain assumptions, sequentially Cohen-Macaulay rings have a trivial Lyubeznik table.…”