Birkhoff type problems were studied by Ringel and Schmidmeier, by
Simson and others. Our approach focusses on categorical structures
(Serre duality, tilitng, Calabi-Yau dimension, ...) of such
problems. We established a link between weighted projective lines of
triple weight type and the classification of invariant flags of
nilpotent operators. In this talk, we will discuss results, techniques
and applications. This is joint work with Helmut Lenzing and Hagen