  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.
