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\(M\)-curves and symmetric products. (English) Zbl 1386.14201
Summary: Let \((X,\sigma )\) be a geometrically irreducible smooth projective \(M\)-curve of genus \(g\) defined over the field of real numbers. We prove that the \(n\)-th symmetric product of \((X, \sigma )\) is an \(M\)-variety for \(n=2, 3\) and \(n \geq 2g -1\).

MSC:
14P25 Topology of real algebraic varieties
14H40 Jacobians, Prym varieties
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