On coherent systems with fixed determinant (Q2874720)

Let \(C\) be a curve (smooth, projective, of genus g) over \(\mathbb C\). ``Recall that a coherent system on \(C\) of type \((r,d,k)\) is a pair \((E,V)\) consisting of a vector bundle \(E\) of rank \(r\) and degree \(d\) and a linear subspace \(V\) of \(H^0(E)\) of dimension \(k\)''. Recently, \textit{B. Osserman} [Int. J. Math. 24, No. 11, Article ID 1350084, 20 p. (2013; Zbl 1287.14017)] obtained lower bounds for the dimension of the moduli spaces of coherent systems on algebraic curves with fixed determinant, in some circumstances which are special cases of a conjecture made in this paper (conjecture 2.3). The object of ``this paper is to show that some of Osserman's bounds are sharp''.