Sur les nœuds de Weierstraß

Gendron, Quentin

Annales Henri Lebesgue, Tome 4 (2021), pp. 571-589.

Cet article donne la description des nœuds des courbes stables qui sont limites de points de Weierstraß. Cela résout le problème posé par Esteves de caractériser les courbes stables dont aucun nœud n’est limite de points de Weierstraß. De plus, nous étendons ce résultat au cas des points de $k$-Weierstraß pour tout $k\ge 1$. Enfin, nous donnons la description des lacunes de points de $k$-Weierstraß réalisées sur des surfaces de Riemann de genre $2$. Les preuves reposent sur la compactification des strates de différentielles introduites par Bainbridge–Chen–Gendron–Grushevsky–Möller.

This article gives the description of the nodes of stable curves which are limits of Weierstraß points. This gives the solution of the problem posed by Esteves of characterising the stable curves that do not have nodes which are limits of Weierstraß points. Moreover, we extend this result to $k$-Weierstraß points for all $k\ge 1$. Finally we describe the $k$-Weierstraß gap sequences that are realised by $k$-Weierstraß points in genus $2$. The proofs rely on the compactification of strata of differentials introduced by Bainbridge–Chen–Gendron–Grushevsky–Möller.

Classification : 14H10, 30F30, 14H55, 14H45
Mots clés : Weierstrass points, Riemann surfaces, stable curves, Weierstrass gap sequences

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