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TMF, 2010, Volume 165, Number 3, Pages 472–487 (Mi tmf6588)  

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

G. F. Helmincka, V. A. Poberezhnyib

a 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: https://doi.org/10.4213/tmf6588

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

Bibliographic databases:

Document Type: Article

Citation: G. F. Helminck, V. A. Poberezhnyi, “Moving poles of meromorphic linear systems on $\mathbb P^1(\mathbb C)$ in the complex plane”, TMF, 165:3 (2010), 472–487; Theoret. and Math. Phys., 165:3 (2010), 1637–1649

Citation in format AMSBIB
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\paper Moving poles of meromorphic linear systems on $\mathbb P^1(\mathbb C)$ in the~complex plane
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\issue 3
\pages 472--487
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\pages 1637--1649
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