Noncommutative Curves of Genus Zero

Investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. This title 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.

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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.