Journal of the
Korean Mathematical Society JKMS

Here we consider bihyperelliptic curves, i.e., double covers of hyperelliptic curves. By applying the theory of quadruple covers, among other things we prove that the bihyperelliptic locus in the moduli space of smooth curves is irreducible and unirational for $g\ge4\gamma+2\ge10$.

Keywords: curves, moduli, cover, unirationality

MSC numbers: 14H10, 14H45, 14E20