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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
##### Keywords:
$$M$$-curve; symmetric product; real locus
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##### References:
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