This article is cited in 1 paper

Moving poles of meromorphic linear systems on $\mathbb P^1(\mathbb C)$ in the complex plane

G. F. Helminck^a, V. A. Poberezhnyi<sup>b

a</sup> Korteweg–de Vries Institute of Mathematics, University of Amsterdam, Amsterdam, The~Netherlands
^b Institute for Theoretical and Experimental Physics, Moscow, Russia

Abstract: 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.

DOI: 10.4213/tmf6588

 English version: Theoretical and Mathematical Physics, 2010, 165:3, 1637–1649

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