Selecta Mathematica

, Volume 23, Issue 3, pp 2243–2259

# Du Val curves and the pointed Brill–Noether Theorem

• Gavril Farkas
• Nicola Tarasca
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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