A survey on the Lyubeznik numbers
  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. 
Luis N\'u\~nez-Betancourt, Emily E. Witt, Wenliang Zhang
math.AC math.AG