Marc Coppens

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20242026

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math.AG2026

Smoothness results for the schemes of special divisors on general k-gonal curves

Marc Coppens

For a general $k$ -gonal curve $C$ with a morphism $f : C \to P^{1}$ of degree $k$ , we consider the refinement of the Brill-Noether schemes $W_{d}^{r} (C)$ by means of the…

math.AG2025

A picture of the irreducible components of $W_{d}^{r} (C)$ for a general $k$ -gonal curve $C$

Marc Coppens

Based on results on Hurwitz-Brill-Noether theory obtained by H. Larson we give a picture of the irreducible components of $W_{d}^{r} (C)$ for a general $k$ -gonal curve of genus $g$ . Thi…

math.AG2024

A study of general Martens-special chains of cycles

Marc Coppens

For a general Martens-special chain of cycles $I^$ of type $k$ we prove that the gonality is equal to $k + 2$ . Although $dim (W_{k + 2}^{1} (I^)) = k$ we prove that $w_{k + 2}^{1} (I^) = 0$ . We…

Smoothness results for the schemes of special divisors on general k-gonal curves

A picture of the irreducible components of Wdr​(C) for a general k-gonal curve C

A study of general Martens-special chains of cycles

A picture of the irreducible components of $W_{d}^{r} (C)$ for a general $k$ -gonal curve $C$