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ISBN 10: 0821844008
ISBN 13: 978-0821844007
Author: Dirk Kussin
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 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 X and the homogeneous prime ideals of height one in R, and these prime ideals are principal in a strong sense.
Chapter 0. Background
Chapter 1. Graded factoriality
Chapter 2. Global and local structure of the sheaf category
Chapter 3. Tubular shifts and prime elements
Chapter 4. Commutativity and multiplicity freeness
Chapter 5. Automorphism groups
Chapter 6. Insertion of weights
Chapter 7. Exceptional objects
Chapter 8. Tubular exceptional curves
Appendix A. Automorphism groups over the real numbers
Appendix B. The tubular symbols
nonsingular curve
noncommutative geometry
a genus is a group of similar
a genus is composed of a number of similar
non-zero genus
Tags: Dirk Kussin, Noncommutative, Curves, Dimensional
