This talk is based on joint work with Martin Herschend, Osamu Iyama, and Hiroyuki Minamoto. Classically, the classes of tame (representation infinite, connected) hereditary algebras and Fano Geigle-Lenzing weighted projective lines coincide up to derived equivalence. With the development of Iyama’s higher AR-theory, and our work on Geigle-Lenzing projective spaces, it has become natural to ask if there is a higher dimensional analogue of this fact. Here dimension refers to, on the one side the global dimension of the algebra, and on the other side the dimension of the space. Unfortunately, so far a general answer (or general strategy) is elusive. In my talk I will focus on the hypersurface case, and more specifically certain weight sequences within the hypersurface case. For these, I will explain how one may find suitable tilting bundles on the Geigle-Lenzing weighted projective space.
This video was produced by Syracuse University Department of Mathematics as part of ICRA 2016.
