Memoirs of the American Mathematical Society 2009; 128 pp; softcover Volume: 201 ISBN10: 0821844008 ISBN13: 9780821844007 List Price: US$67 Individual Members: US$40.20 Institutional Members: US$53.60 Order Code: MEMO/201/942
 In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve \(\mathbb{X}\) admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain \(R\) in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of \(\mathbb{X}\) and the homogeneous prime ideals of height one in \(R\), and these prime ideals are principal in a strong sense. Table of Contents Part 1. The homogeneous case  Graded factoriality
 Global and local structure of the sheaf category
 Tubular shifts and prime elements
 Commutativity and multiplicity freeness
 Automorphism groups
Part 2. The weighted case  Insertion of weights
 Exceptional objects
 Tubular exceptional curves
 Appendix A. Automorphism groups over the real numbers
 Appendix B. The tubular symbols
 Bibliography
 Index
