# Emanuele Delucchi: Supersolvable posets and the K(\pi,1) property for Abelian arrangements.

Time: Wed 2021-06-09 10.15 - 11.15

Location:

Lecturer: Emanuele Delucchi (IDSIA-SUPSI e Università di Pisa)

### Abstract

I will introduce a generalized notion of supersolvability for locally geometric posets. In the case of posets of layers of abelian arrangements it gives an equivalent characterization of the existence of an iterated fibration of the arrangement's complement. For arrangements in complex tori and products of elliptic curves, this implies the $$K(\pi,1)$$ property. In the case of geometric lattices we recover Stanley's classical definition as well as the familiar theory of fiber-type arrangements due to Terao and Falk-Randell. However, the combinatorial and topological underpinnings of our generalized supersolvability are subtle.

The talk will start with a review of the necessary background on posets and arrangements. Then I will present the combinatorial definition and its topological implications for abelian arrangements. I will also discuss some results and open questions about the structural relationship with the classical combinatorial notion.

This is joint work with Christin Bibby

Zoom meeting ID: 654 5562 3260