Du Val curves and the pointed Brill–Noether Theorem

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 expli...

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Bibliographic Details
Published in:Selecta mathematica (Basel, Switzerland) Switzerland), 2017-07, Vol.23 (3), p.2243-2259
Main Authors: Farkas, Gavril, Tarasca, Nicola
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Theorems
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Summary: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.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-017-0329-3