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Du Val curves and the pointed Brill-Noether Theorem

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arxiv 1606.02725 v4 pith:XOW7IRUD submitted 2016-06-08 math.AG

Gavril Farkas , Nicola Tarasca This is my paper · ORCID
classification math.AG
keywords curvespointedbrill-noetherexplicitcurvegeneraltheoremarbitrary
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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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  1. The Geometric Syzygy Conjecture in Positive Characteristic

    math.AG 2025-08 conditional novelty 7.0 of 10

    The Geometric Syzygy Conjecture holds for general canonical curves over algebraically closed fields of characteristic at least 2g-4.

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