On coherent systems with fixed determinant

Over the past 20 years, a great deal of work has been done on the moduli spaces of coherent systems on algebraic curves. Until recently, however, there has been very little work on the fixed determinant case, except for the special case of rank 2 and canonical determinant. This situation has changed due to two papers of B. Osserman, who has obtained lower bounds for the dimensions of the fixed determinant moduli spaces in some cases. Our object in this paper is to show that some of Osserman's bounds are sharp.