On the rationality of certain Weierstrass spaces of type (5, g)
Tóm tắt
Let
$${\mathfrak{M}_g}$$
be the moduli space of smooth, integral curves of genus g over the complex field
$${\mathbb{C}}$$
and denote by
$${\overline{W}_{d,g} \subseteq\mathfrak{M}_g}$$
the Weierstrass space of type (d, g), i.e. the closure of the locus of points representing d-gonal with exactly one total ramification point, the other ramification points being simple. The locus
$${\overline{W}_{d,g}}$$
is always irreducible and it is rational for d = 2, 3, 4. We prove here the rationality of
$${\overline{W}_{5,g}}$$
for g ≡ 16 (mod 20).
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