Local cohomology modules with support in 2-regular monomial ideals. Applications to the topology of arrangements of linear spaces.

A large class of arrangements of linear spaces are defined by 2-regular monomial ideals in a polynomial ring. Local cohomology modules with support on monomial ideals is a field of active research, and there are some algorithms to make effective the study of local cohomology modules.

In this lecture we study the local cohomology modules with support on 2-regular monomial ideals by using independent methods. We can describe the structure of local cohomology modules not only effective but explicit from the minimal prime decomposition of 2-regular monomial ideal by simple inspection. A special case of 2-regular monomial ideals are provided by the Ferrer diagrams.
As a consequence in the characteristic zero case, we can get their characteristic class (like D-modules) and the topology of the complement of an arrangement of linear spaces.