Du Val curves and the pointed Brill–Noether Theorem

• Gavril Farkas ^[1] ; Nicola Tarasca ^[2]
  1. [1] Humboldt University of Berlin

     Humboldt University of Berlin

     Berlin, Stadt, Alemania

     
  2. [2] University of Utah

     University of Utah

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 3, 2017, págs. 2243-2259
• Idioma: inglés
• DOI: 10.1007/s00029-017-0329-3
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We show that a general curve in an explicit class of what we call Du Val pointed curves satisfies the Brill–Noether Theorem for pointed curves. Furthermore, we prove that a generic pencil of Du Val pointed curves is disjoint from all Brill– Noether divisors on the universal curve. This provides explicit examples of smooth pointed curves of arbitrary genus defined over Q which are Brill–Noether general. A similar result is proved for 2-pointed curves as well using explicit curves on elliptic ruled surfaces.