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Title:Noncommutative curves
Abstract: Noncommutative projective geometry studies noncommutative graded rings by replacing the variety by a suitable Grothendieck category. One way of studying the resulting category is to examine the full subcategories which behave like curves on a commutative variety. Smith and Zhang initiated such a study by considering the subcategory generated by a particular type of module they called a ``pure curve module in good position.'' In order to extend the applicability of this approach, the definition of pure curve modules in good position was generalized to modules called ``multistrand'' modules. The categories created from multistrand modules are described and shown (in general) to be different from the type of category created from a pure curve module in good position. |