Homologically trivial integrable deformations of germs of holomorphic functions
Journal of Singularities, Tome 24 (2022), pp. 119-125
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We study analytic deformations by integrable 1-forms a germ of a holomorphic function at the origin of the complex affine space in dimension three or higher. We prove that, under some mild nondegeneracy conditions on the function germ, the existence of a simple normal form for the deformation is equivalent to a homological condition: the annihilation of the deformed one-form in the first homology group of the non-singular fibers of the function germ. In many cases this implies the existence of a holomorphic first integral for the deformation.
@article{10_5427_jsing_2022_24d,
author = {Victor Le\'on and Bruno Sc\'ardua},
title = {Homologically trivial integrable deformations of germs of holomorphic functions},
journal = {Journal of Singularities},
pages = {119--125},
publisher = {mathdoc},
volume = {24},
year = {2022},
doi = {10.5427/jsing.2022.24d},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.24d/}
}
TY - JOUR AU - Victor León AU - Bruno Scárdua TI - Homologically trivial integrable deformations of germs of holomorphic functions JO - Journal of Singularities PY - 2022 SP - 119 EP - 125 VL - 24 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.24d/ DO - 10.5427/jsing.2022.24d ID - 10_5427_jsing_2022_24d ER -
%0 Journal Article %A Victor León %A Bruno Scárdua %T Homologically trivial integrable deformations of germs of holomorphic functions %J Journal of Singularities %D 2022 %P 119-125 %V 24 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.24d/ %R 10.5427/jsing.2022.24d %F 10_5427_jsing_2022_24d
Victor León; Bruno Scárdua. Homologically trivial integrable deformations of germs of holomorphic functions. Journal of Singularities, Tome 24 (2022), pp. 119-125. doi: 10.5427/jsing.2022.24d
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