Séminaire Algèbre Géométrie Algébrique Topologie Algébrique :

Le 09 janvier 2003 à - salle 431

Présentée par Huiszgen Zimmermann Birge - University of Santa Barbara

Finite Dimensional Representation Theory by way of Grassmannians, I

Part I. The classical affine varieties of representations: Problems they solve and problems they trigger Among other examples, we discuss the pivotal class of path algebras of quivers and their representation types, which will lead to introduction and first applications of the classical module varieties (theorems of Gabriel, Nazarova, Kac). The geometric pictures of categories of modules raised far-reaching problems in their own right, in particular those of `degenerations' and `moduli spaces'. We will explain these problems and some solutions in specialized contexts. I will discuss a new approach to these conjectures using infinite dimensional tilting modules. Hereby I will present joint work with Jan Trlifaj.