Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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