Lorenzo Vecchi: Inductive and divisional posets

Abstract: A classical problem by Terao in the theory of hyperplane arrangements is determining whether freeness is a combinatorial property, i.e. if it only depends on the poset of intersections. One appealing feature of this property for combinatorialists is that it implies that the characteristic polynomial is factorable, i.e. it has only non-negative integer roots. In pursue of a notion of freeness for abelian arrangements, we define the notion of inductive and divisional posets. We show that these classes of posets are factorable and contain the class of strictly supersolvable posets introduced by Bibby and Delucchi. As an application, we show inductiveness (hence, factorability) of any toric arrangement coming from ideals of root systems in type A, B or C.

This is joint work with Roberto Pagaria, Maddalena Pismataro, Tan Nhat Tran.