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arXiv · 1606.02725

Du Val curves and the pointed Brill-Noether Theorem

Gavril Farkas·Nicola Tarasca
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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 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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Gavril Farkas, Nicola Tarasca. 2016-06-08. Du Val curves and the pointed Brill-Noether Theorem. https://doi.org/10.1007/s00029-017-0329-3

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