A survey on the Lyubeznik numbers

TL;DR

This survey reviews the properties, significance, and recent developments related to Lyubeznik numbers, which are invariants of local rings with connections to geometry and topology.

Contribution

It provides a comprehensive overview of Lyubeznik numbers, highlighting their properties, recent advances, and generalizations in the field.

Findings

Lyubeznik numbers are invariants capturing algebraic and geometric properties.

Recent developments include generalizations and new results in the area.

The survey summarizes key properties and connections to other mathematical fields.

Abstract

The Lyubeznik numbers are invariants of a local ring containing a field that capture ring-theoretic properties, but also have numerous connections to geometry and topology. We discuss basic properties of these integer-valued invariants, as well as describe some significant results and recent developments (including certain generalizations) in the area.