Resumen de On the rationality of certain Weierstrass spaces of type (5, g)

G. Casnati

• Let ?? be the moduli space of smooth, integral curves of genus g over the complex field ℂ and denote by ?⎯⎯⎯⎯⎯⎯⎯?,?⊆?? 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 ?⎯⎯⎯⎯⎯⎯⎯?,? is always irreducible and it is rational for d = 2, 3, 4. We prove here the rationality of ?⎯⎯⎯⎯⎯⎯⎯5,? for g ≡ 16 (mod 20).