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The moduli space R_{g,2n} parametrizes double covers of smooth curves ofgenus g ramified at 2n points. We will prove the (uni)rationality of R_{g,2},R_{g,4} and R_{g,6} in low genera.

(Uni)rational parametrizations of $\mathcal R_{g,2}$, $\mathcal R_{g,4}$ and $\mathcal R_{g,6}$ in low genera