Du Val curves and the pointed Brill–Noether Theorem

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.

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Correspondence to Nicola Tarasca.

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Farkas, G., Tarasca, N. Du Val curves and the pointed Brill–Noether Theorem. Sel. Math. New Ser. 23, 2243–2259 (2017). https://doi.org/10.1007/s00029-017-0329-3

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Keywords

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

Mathematics Subject Classification

  • 14H99 (primary)
  • 14J26 (secondary)