Rationality of moduli spaces of stable bundles on curves over \(\mathbb{R}\) (Q2331562)

The authors study stable vector bundles defined over \(\mathbb{R}\) on a smooth projective curve \(C\) of genus \(g\) defined over \(\mathbb{R}\) and with \(C(\mathbb{R})=\emptyset\). Fix a real line bundle \(L\) on \(C\). Let \(M_{r,L}\) denotes the moduli space of rank \(r\) stable bundles \(E\) on \(C\) with \(\det (E)\cong L\). The authors classify the birational type of \(M_{r,L}\). The main tools are the papers [\textit{A. King} and \textit{A. Schofield}, Indag. Math., New Ser. 10, No. 4, 519--535 (1999; Zbl 1043.14502)] and [\textit{N. Hoffmann}, Int. Math. Res. Not. 2007, No. 3, Article ID rnm010, 30 p. (2007; Zbl 1127.14031)].