Rank-two vector bundles on Halphen surfaces and the Gauss-Wahl map for du Val curves
[Fibrés vectoriels de rang 2 sur les surfaces de Halphen et application de Gauss-Wahl pour les courbes de du Val]
Journal de l’École polytechnique — Mathématiques, Tome 4 (2017), pp. 257-285.

Une courbe de du Val de genre g est une courbe plane de degré 3g ayant 8 points de multiplicité g, un point de multiplicité g-1 et pas d’autre singularité. Nous montrons que le corang de l’application de Gauss-Wahl pour une courbe de du Val générale de genre impair (>11) est égal à 1. Ceci, joint aux résultats de [1], montre que la caractérisation, obtenue dans [3], des courbes de Brill-Noether-Petri ayant une application de Gauss-Wahl non surjective comme sections hyperplanes de surfaces K3 et limites de celles-ci, est optimale.

A genus-g du Val curve is a degree-3g plane curve having 8 points of multiplicity g, one point of multiplicity g-1, and no other singularity. We prove that the corank of the Gauss-Wahl map of a general du Val curve of odd genus (>11) is equal to one. This, together with the results of [1], shows that the characterization of Brill-Noether-Petri curves with non-surjective Gauss-Wahl map as hyperplane sections of K3 surfaces and limits thereof, obtained in [3], is optimal.

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DOI : https://doi.org/10.5802/jep.43
Classification : 14J28,  14H51
Mots clés : Courbes, surfaces K3, fibrés vectoriels 
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     title = {Rank-two vector bundles on {Halphen} surfaces and the {Gauss-Wahl} map for du {Val} curves},
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Arbarello, Enrico; Bruno, Andrea. Rank-two vector bundles on Halphen surfaces and the Gauss-Wahl map for du Val curves. Journal de l’École polytechnique — Mathématiques, Tome 4 (2017), pp. 257-285. doi : 10.5802/jep.43. http://www.numdam.org/articles/10.5802/jep.43/

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