Noncommutative Curves of Genus Zero: Related to Finite Dimensional Algebras (Memoirs of the American Mathematical Society)
Noncommutative Curves of Genus Zero: Related to Finite Dimensional Algebras (Memoirs of the American Mathematical Society) by Dirk Kussin
English | 2009 | ISBN: 0821844008 | 128 Pages | PDF | 1.93 MB
English | 2009 | ISBN: 0821844008 | 128 Pages | PDF | 1.93 MB
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.