Séminaire Algèbre Géométrie Algébrique Topologie Algébrique :

Le 16 janvier 2003 à - salle 431

Présentée par Huiszgen Zimmermann Birge - University of Santa Barbara

Finite Dimensional Representation Theory by way of Grassmannians, II

Part II. Grassmannian varieties of representations In recent work (partly joint with K. Bongartz), it surfaced that the problems we posed at the end of the first talk can be more effectively tackled by way of smaller, combinatorially and computationally more accessible, projective varieties. The first half of the lecture will be devoted to introducing and understanding these Grassmannian varieties; the second will return to the questions concerning degenerations and moduli spaces. In particular, we will give graphical examples of the classes of degenerations which can be obtained with the help of the `new' varieties. Finally, we will come full circle and show how the Grassmannians lend themselves to a better understanding of representation types of certain module categories. I will discuss a new approach to these conjectures using infinite dimensional tilting modules. Hereby I will present joint work with Jan Trlifaj.