Extremal properties of concealed-canonical algebras

Canonical algebras, introduced by C.M. Ringel in 1984, play an important role in the representation theory of finite dimensional algebras. They are equipped with a large contact surface to many further mathematical subjects like function theory, 3-manifolds, singularity theory, commutative algebra and algebraic geometry. We show in this paper that canonical algebras are characterized by a number of interesting extremal properties (among the class of endomorphism rings of tilting bundles on a weighted projective line). We also study the corresponding class of algebras antipodal to canonical ones. Our study sheds new insight in the nature of concealed-canonical algebras, and sheds light on an old question: Why are the canonical algebras canonical?