Abstract
Let C be a smooth, projective, geometrically irreducible curve defined over R such that C(R)=∅. Let r>0 and d be integers which are coprime. Let L be a line bundle on C which corresponds to an R point of PicC/Rd. Let Mr,L be the moduli space of stable bundles on the complexification of C of rank r and determinant L. We classify birational types of Mr,L over R.
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