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

• Autores: G. Casnati
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 62, Fasc. 2, 2011, págs. 225-238
• Idioma: inglés
• DOI: 10.1007/s13348-010-0009-5
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• Resumen

  • 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).