DMM Seminar

Speaker: Osamu Iyama (Nagoya U)
Title: Tilting theory on Geigle-Lenzing weighted projective spaces
Date (JST): Mon, Oct 07, 2013, 14:00 - 17:00
Place: Seminar Room A
Abstract: Weighted projective lines, introduced by Geigle and Lenzing in 1987, are one of the basic objects in representation theory. One key property is that they have tilting bundles, whose endomorphism rings are canonical algebras introduced by Ringel.
In this talk we will introduce Geigle-Lenzing d-spaces as a higher dimensional analog of weighted projective lines. We show that there is a nice tilting bundle, which generalizes results by Beilinson, Geigle-Lenzing, Baer and Ishii-Ueda.
The endomorphism algebra of the tilting bundle is called a d-canonical algebra, and closely related to d-representation infinite algebras in higher dimensional Auslander-Reiten theory.
We will then discuss Cohen-Macaulay representation theory of Geigle-Lenzing d-spaces. Using Orlov-type semiorthogonal decomposition, we show that the singular derived category also has a tilting object, which generalizes results by Kussin-Meltzer-Lenzing and Futaki-Ueda.
This talk is based on joint works with Martin Herschend, Boris Lerner, Hiroyuki Minamoto and Steffen Oppermann.
Remarks: 14:00-15:00 (Part I)
15:30-17:00 (Part II)