On etude l’espace des courbes holomorphes a bord dans une surface reelle situe dans une fibree vectoriel de rang 2 sur une variete reelle a dimension deux. On prouve que, si le fibree ambient admet une action transitive et holomorphe qui preserve la fibration, alors une section avec un et seulement un point complexe admet des deformation petits dans la norme tel que toute disque holomorphe a bord dans la deformation soit Fredholm reguliere. On prouve aussi la Fredholm regularite dans le cas que le fibree ambient est Kaehlerien a signature (2,2), l’action de la groupe e holomorphe et symplectique, et la surface bordante est Lagrangienne avec un seul poit complexe.
We study the space of holomorphic discs with boundary on a surface in a real 2-dimensional vector bundle over a compact 2-manifold. We prove that, if the ambient 4-manifold admits a fibre-preserving transitive holomorphic action, then a section with a single complex point has -close sections such that any (non-multiply covered) holomorphic disc with boundary in these sections are Fredholm regular. Fredholm regularity is also established when the complex surface is neutral Kähler, the action is both holomorphic and symplectic, and the section is Lagrangian with a single complex point.
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@article{AFST_2020_6_29_3_565_0,
author = {Brendan Guilfoyle and Wilhelm Klingenberg},
title = {Fredholm-Regularity of {Holomorphic} {Discs} in {Plane} {Bundles} over {Compact} {Surfaces}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {565--576},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 29},
number = {3},
year = {2020},
doi = {10.5802/afst.1639},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1639/}
}
TY - JOUR AU - Brendan Guilfoyle AU - Wilhelm Klingenberg TI - Fredholm-Regularity of Holomorphic Discs in Plane Bundles over Compact Surfaces JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2020 SP - 565 EP - 576 VL - 29 IS - 3 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1639/ DO - 10.5802/afst.1639 LA - en ID - AFST_2020_6_29_3_565_0 ER -
%0 Journal Article %A Brendan Guilfoyle %A Wilhelm Klingenberg %T Fredholm-Regularity of Holomorphic Discs in Plane Bundles over Compact Surfaces %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2020 %P 565-576 %V 29 %N 3 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1639/ %R 10.5802/afst.1639 %G en %F AFST_2020_6_29_3_565_0
Brendan Guilfoyle; Wilhelm Klingenberg. Fredholm-Regularity of Holomorphic Discs in Plane Bundles over Compact Surfaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 3, pp. 565-576. doi : 10.5802/afst.1639. https://afst.centre-mersenne.org/articles/10.5802/afst.1639/
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