The second vanishing theorem in Stanley-Reisner ring with topological interpretation

TL;DR

This paper extends the second vanishing theorem for local cohomology to Stanley-Reisner rings, providing a topological interpretation that links algebraic properties with combinatorial topology.

Contribution

It introduces a new vanishing theorem for Stanley-Reisner rings and offers a topological perspective, bridging algebraic and combinatorial topology.

Findings

Established a vanishing theorem for Stanley-Reisner rings

Connected algebraic vanishing results with topological interpretations

Enhanced understanding of local cohomology in combinatorial contexts

Abstract

For regular local ring, the ``second vanishing theorem'' or ``SVT'' of local cohomology has been proved in several cases. In this paper, we explore the result similar to that of the SVT to Stanley-Reisner ring with an interpretation from combinatorial topology.