Thiago Holleben: Rees algebras and Lefschetz properties of squarefree monomial ideals

Abstract.

In Combinatorics, a common problem is to show that certain sequences are unimodal (i.e, they increase up to a point, and then decrease). One way of proving that a sequence is unimodal is by showing that certain artinian rings satisfy a property called weak Lefschetz property (WLP). In this talk, we study the WLP of a specific artinian reduction of squarefree monomial ideals. More specifically, we use two known ways of associating squarefree monomial ideals to simplicial complexes to study connections between Lefschetz properties and Rees algebras. As a consequence, we show that a large family of squarefree monomial ideals are not normally torsion-free.