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 Q which are Brill-Noether general. A similar result is proved for 2-pointed curves as well using explicit curves on elliptic ruled surfaces.

14 pages, appeared in Selecta Mathematica. Slight inaccuracy in Section 2.1 corrected

References in corpus (1)

• The Prym-Green Conjecture for torsion bundles of high order

Cited by in corpus (2)

• K-classes of Brill-Noether loci and a determinantal formula
• The resolution of paracanonical curves of odd genus