Du Val curves and the pointed Brill-Noether Theorem
Algebraic Geometry
2023-03-10 v4
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.
Keywords
Cite
@article{arxiv.1606.02725,
title = {Du Val curves and the pointed Brill-Noether Theorem},
author = {Gavril Farkas and Nicola Tarasca},
journal= {arXiv preprint arXiv:1606.02725},
year = {2023}
}
Comments
14 pages, appeared in Selecta Mathematica. Slight inaccuracy in Section 2.1 corrected