[Fibrés vectoriels de rang sur les surfaces de Halphen et application de Gauss-Wahl pour les courbes de du Val]
Une courbe de du Val de genre est une courbe plane de degré ayant points de multiplicité , un point de multiplicité 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 () est égal à . 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- du Val curve is a degree- plane curve having 8 points of multiplicity , one point of multiplicity , and no other singularity. We prove that the corank of the Gauss-Wahl map of a general du Val curve of odd genus () 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.
Accepté le :
Publié le :
DOI : 10.5802/jep.43
Keywords: Curves, K3 surfaces, vector bundles
Mot clés : Courbes, surfaces K3, fibrés vectoriels
Enrico Arbarello 1 ; Andrea Bruno 2
CC-BY-ND 4.0
@article{JEP_2017__4__257_0,
author = {Enrico Arbarello and Andrea Bruno},
title = {Rank-two vector bundles on {Halphen} surfaces and the {Gauss-Wahl} map for du {Val} curves},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {257--285},
publisher = {\'Ecole polytechnique},
volume = {4},
year = {2017},
doi = {10.5802/jep.43},
zbl = {1368.14050},
mrnumber = {3623355},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.43/}
}
TY - JOUR AU - Enrico Arbarello AU - Andrea Bruno TI - Rank-two vector bundles on Halphen surfaces and the Gauss-Wahl map for du Val curves JO - Journal de l’École polytechnique — Mathématiques PY - 2017 SP - 257 EP - 285 VL - 4 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.43/ DO - 10.5802/jep.43 LA - en ID - JEP_2017__4__257_0 ER -
%0 Journal Article %A Enrico Arbarello %A Andrea Bruno %T Rank-two vector bundles on Halphen surfaces and the Gauss-Wahl map for du Val curves %J Journal de l’École polytechnique — Mathématiques %D 2017 %P 257-285 %V 4 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.43/ %R 10.5802/jep.43 %G en %F JEP_2017__4__257_0
Enrico Arbarello; Andrea Bruno. 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. https://jep.centre-mersenne.org/articles/10.5802/jep.43/
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