Moving poles of meromorphic linear systems on $\mathbb P^1(\mathbb C)$ in the~complex plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 3, pp. 472-487
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Let $E^0$ be a holomorphic vector bundle over $\mathbb P^1(\mathbb C)$ and $\nabla^0$ be a meromorphic connection of $E^0$. We introduce the notion of an integrable connection that describes the movement of the poles of $\nabla^0$ in the complex plane with integrability preserved. We show the that such a deformation exists under sufficiently weak conditions on the deformation space. We also show that if the vector bundle $E^0$ is trivial, then the solutions of the corresponding nonlinear equations extend meromorphically to the deformation space.
Keywords:
integrable connection, deformation space, integrable deformation, logarithmic pole.
@article{TMF_2010_165_3_a4,
author = {G. F. Helminck and V. A. Poberezhnyi},
title = {Moving poles of meromorphic linear systems on $\mathbb P^1(\mathbb C)$ in the~complex plane},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {472--487},
publisher = {mathdoc},
volume = {165},
number = {3},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2010_165_3_a4/}
}
TY - JOUR AU - G. F. Helminck AU - V. A. Poberezhnyi TI - Moving poles of meromorphic linear systems on $\mathbb P^1(\mathbb C)$ in the~complex plane JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2010 SP - 472 EP - 487 VL - 165 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2010_165_3_a4/ LA - ru ID - TMF_2010_165_3_a4 ER -
%0 Journal Article %A G. F. Helminck %A V. A. Poberezhnyi %T Moving poles of meromorphic linear systems on $\mathbb P^1(\mathbb C)$ in the~complex plane %J Teoretičeskaâ i matematičeskaâ fizika %D 2010 %P 472-487 %V 165 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2010_165_3_a4/ %G ru %F TMF_2010_165_3_a4
G. F. Helminck; V. A. Poberezhnyi. Moving poles of meromorphic linear systems on $\mathbb P^1(\mathbb C)$ in the~complex plane. Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 3, pp. 472-487. http://geodesic.mathdoc.fr/item/TMF_2010_165_3_a4/