A counter example of Arrondo-Sols' conjecture (Q1202817)

Arrondo-Sol's conjecture can be stated as follows: Let \(E\) be a rank-2 vector bundle of degree \(d\) on a smooth complex algebraic curve of genus \(g\), \(-e\) be the minimal self-intersection number of a unisecant curve in the ruled surface \(p(E)\), and \(r+1=h^ 0(E)\). If \(-e \leq d \leq 4g-4+e\) and \(E \neq L \oplus L\) \((L\) line subbundle), then \(r \leq(d+e)/2\) [cf. \textit{E. Arrondo} and \textit{I. Sols} in Complex projective geometry, Sel. Pap. Conf. Proj. Var., Trieste 1989, and Vector Bundles and Special Proj. Embeddings, Bergen 1989, Lond. Math. Soc. Lect. Note Ser. 179, 24-31 (1992; Zbl 0772.14012)]. -- If the curve is hyperelliptic, then the conjecture is true (loc. cit.). The paper under review shows, by an example, that the conjecture is false for nonhyperelliptic curves of genus 3.