Generic modules have been introduced by Crawley-Boevey in order to provide a better understanding of nite dimensional algebras of tame representation type. In fact he has shown that the generic modules correspond to the one-parameter families of indecomposable nite dimensional modules over a tame algebra 5]. The Second Brauer-Thrall Conjecture provides another reason to study generic modules be...

The purpose of this note is to characterize the finite Hilbert functions which force all of their artinian algebras to enjoy the Weak Lefschetz Property (WLP). Curiously, they turn out to be exactly those (characterized by Wiebe in [W i]) whose Gotzmann ideals have the WLP. This implies that, if a Gotzmann ideal has the WLP, then all algebras with the same Hilbert function (and hence lower Bett...

This note provides a self-contained exposition of the proof of the artinian conjecture, following closely Djament’s Bourbaki lecture. The original proof is due to Putman, Sam, and Snowden.