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Selecta Mathematica

, Volume 23, Issue 3, pp 2243–2259 | Cite as

Du Val curves and the pointed Brill–Noether Theorem

  • Gavril Farkas
  • Nicola TarascaEmail author
Article

Abstract

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 \({\mathbb {Q}}\) which are Brill–Noether general. A similar result is proved for 2-pointed curves as well using explicit curves on elliptic ruled surfaces.

Keywords

Brill–Noether general smooth pointed curves Du Val curves Rational and ruled surfaces 

Mathematics Subject Classification

14H99 (primary) 14J26 (secondary) 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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